Showing posts with label Exponents. Show all posts
Showing posts with label Exponents. Show all posts

S.chand Class 8 Maths Solution Chapter 2 Exponents Exercise 2B

 Exercise 2B

Q1 | Ex-2B | Class 8 | SChand | Composite Maths | Exponents | Chapter 2 | myhelper

Question 1

Express as a rational number :

(i) $5^{-1}$

(ii) $\left(\frac{1}{2}\right)^{-6}$

(iii) $\left(\frac{3}{4}\right)^{-4}$

(iv) $\left(-\frac{4}{5}\right)^{-2}$

(v) $(-x)^{-1}$

Sol :






Q2 | Ex-2B | Class 8 | SChand | Composite Maths | Exponents | Chapter 2 | myhelper

Question 2

Simplify and express with positive exponents :

(i) $\left(\frac{4}{9}\right)^{-3} \times\left(\frac{4}{9}\right)^{11} \times\left(\frac{4}{9}\right)^{-10}$

(ii) $\left(-\frac{7}{11}\right)^{-6} \div\left(\frac{-7}{11}\right)^{-2}$

(iii) $\left(\frac{-8}{3}\right)^{-7} \div\left(\frac{-8}{3}\right)^{4}$

(iv) $\left[\left(\frac{9}{11}\right)^{-3} \times\left(\frac{9}{11}\right)^{-7}\right] \div\left(\frac{9}{11}\right)^{-3}$

(v) $\left[\left(\frac{3}{5}\right)^{-2}\right]^{-4}$

(vi) $\left[\left\{\left(-\frac{2}{3}\right)^{-3}\right\}^{-4}\right]^{-2}$

Sol :






Q3 | Ex-2B | Class 8 | SChand | Composite Maths | Exponents | Chapter 2 | myhelper

Question 3

Evaluate :

(i) $\left(\frac{-3}{4}\right)^{-2} \times\left(\frac{-6}{5}\right)^{-2}$

(ii) $\left(\frac{11}{7}\right)^{-4} \times\left(\frac{7}{44}\right)^{-4}$

(iii) $(-16)^{-3} \times\left(\frac{1}{20}\right)^{-3}$

Sol :







Q4 | Ex-2B | Class 8 | SChand | Composite Maths | Exponents | Chapter 2 | myhelper

Question 4

Evaluate :

(i) $\left(3^{-1} \div 4^{-1}\right)^{2}$

(ii) $\left(4^{-1}+8^{-1}\right) \div\left(\frac{2}{3}\right)^{-1}$

(iii) $\left(\frac{2}{3}\right)^{-2} \times\left(\frac{3}{4}\right)^{-3} \times\left(\frac{-7}{8}\right)^{0}$

(iv) $\left(-\frac{1}{4}\right)^{-3} \div\left(\frac{3}{8}\right)^{-2}$

Sol :






Q5 | Ex-2B | Class 8 | SChand | Composite Maths | Exponents | Chapter 2 | myhelper

Question 5

Find x such that :

(i) $\left(\frac{7}{4}\right)^{-3} \times\left(\frac{7}{4}\right)^{-5}=\left(\frac{7}{4}\right)^{x-2}$

(ii) $\left(\frac{125}{8}\right) \times\left(\frac{125}{8}\right)^{x}=\left(\frac{5}{2}\right)^{18}$

Sol :







Q6 | Ex-2B | Class 8 | SChand | Composite Maths | Exponents | Chapter 2 | myhelper

Question 6

Find the reciprocal of the following rational numbers :

(i) $\left(\frac{-3}{7}\right)^{-3} \div\left(\frac{-3}{7}\right)^{-4}$

(ii) $\left(\left(\frac{8}{11}\right)^{2}\right)^{-5} \times\left(\frac{11}{8}\right)^{-12}$

Sol :






Q7 | Ex-2B | Class 8 | SChand | Composite Maths | Exponents | Chapter 2 | myhelper

Question 7

If $3^{2 x+1} \div 9=27$, find x,

Sol :




Q8 | Ex-2B | Class 8 | SChand | Composite Maths | Exponents | Chapter 2 | myhelper

Question 8

By what number should $\left(\frac{-3}{2}\right)^{-3}$ be multiplied, so that the product is $\left(\frac{9}{8}\right)^{-2}$ ?

Sol :




Q9 | Ex-2B | Class 8 | SChand | Composite Maths | Exponents | Chapter 2 | myhelper

Question 9

By what number should $\left(\frac{5}{4}\right)^{-2}$ be divided. so that the quotient $\left(\frac{1}{2}\right)^{-3}$ ?

Sol :



Q10 | Ex-2B | Class 8 | SChand | Composite Maths | Exponents | Chapter 2 | myhelper

Question 10

Simplify $\left[\left\{\left(\frac{-2}{5}\right)^{-7} \times\left(\frac{-2}{5}\right)^{9}\right\} \div\left(\frac{-2}{5}\right)^{2}\right]$ and express the result as a power of 5 .

Sol :





Q11 | Ex-2B | Class 8 | SChand | Composite Maths | Exponents | Chapter 2 | myhelper

Question 11

Simplify :

(i) $\left[\left(-\frac{1}{3}\right)^{8} \div\left(-\frac{1}{3}\right)^{5}\right]-\left[\left(\frac{-1}{3}\right)^{5} \div\left(\frac{-1}{3}\right)^{3}\right]$

(ii) $\left(2^{-1} \div \5^{-1}\right)^{2} \times\left(\frac{-5}{8}\right)^{-2}$

Sol :




Q12 | Ex-2B | Class 8 | SChand | Composite Maths | Exponents | Chapter 2 | myhelper

Question 12

Write the following numbers in scientific notation :

(i) 0.00002

(ii) 0.00000542

(iii) 0.000000093

(iv) 0.003142

Sol :



Q13 | Ex-2B | Class 8 | SChand | Composite Maths | Exponents | Chapter 2 | myhelper

Question 13

Write the following numbers in standard form :

(i) $6 \times 10^{-5}$

(ii) $5.32 \times 10^{-4}$

(iii) $9.6 \times 10^{-8}$

(iv) $2.102 \times 10^{-3}$

Sol :




Q14 | Ex-2B | Class 8 | SChand | Composite Maths | Exponents | Chapter 2 | myhelper

Question 14

Compare : Fill in the blanks with < , > or =

(i) $2.3 \times 10^{-6}.......4.65 \times 10^{-5}$

(ii) $7 \times 10^{-20}.......9 \times 10^{-21}$

Sol :




Multiple Choice Questions (MCQs)

Q15 | Ex-2B | Class 8 | SChand | Composite Maths | Exponents | Chapter 2 | myhelper

Question 15

$\left[4^{-1}+6^{-1}+8^{-1}\right]^{0}$ equals

(a) $1 \frac{11}{13}$

(b) 0

(c) 1

(d) $\frac{-13}{24}$

Sol :





Q16 | Ex-2B | Class 8 | SChand | Composite Maths | Exponents | Chapter 2 | myhelper

Question 16

If $x=\left(\frac{5}{8}\right)^{-2} \times\left(\frac{12}{15}\right)^{-2}$, then the value of $x^{-3}$ is

(a) $\frac{1}{8}$

(b) 64

(c) 8

(d) $\frac{1}{64}$

Sol :





Q17 | Ex-2B | Class 8 | SChand | Composite Maths | Exponents | Chapter 2 | myhelper

Question 17

Solve for $x: 81^{-2} \div 729^{1-x}=9^{2 x}$

(a) 2

(b) -2

(c) 7

(d) -7

Sol :





Q18 | Ex-2B | Class 8 | SChand | Composite Maths | Exponents | Chapter 2 | myhelper

Question 18

The thickness of a soap bubble is about 0.000004 metres. Write the thickness in scientific notation.

(a) $4 \times 10^{-7} \mathrm{~m}$

(b) $4 \times 10^{-5} \mathrm{~m}$

(c) $4 \times 10^{-6} \mathrm{~m}$

(d) $0.4 \times 10^{-5} \mathrm{~m}$

Sol :




Q19 | Ex-2B | Class 8 | SChand | Composite Maths | Exponents | Chapter 2 | myhelper

Question 19

$\left(6 \times 10^{-2}+4.9 \times 10^{-4}\right)$ equals

(a) 0.006049

(b) $6.049 \times 10^{-1}$

(c) $6.049 \times 10^{-2}$

(d) 0.06049

Sol :






High Order Thinking Skills (HOTS)


Q20 | Ex-2B | Class 8 | SChand | Composite Maths | Exponents | Chapter 2 | myhelper

Question 20

Simplify :

(i) $\frac{1}{1+a^{n-m}}+\frac{1}{1+a^{m-n}}$

(ii) $\frac{\left(x^{a+b}\right)^{2} \times\left(x^{b+c}\right)^{2} \times\left(x^{c+a}\right)^{2}}{\left(x^{a} \cdot x^{b} \cdot x^{c}\right)^{3}}$

Sol :





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S.chand Class 8 Maths Solution Chapter 2 Exponents Exercise 2A

  Exercise 2A

Q1 | Ex-2A | Exponents |Class 8 | Schand composite mathematics| Chapter 2 | myhelper

Question 1

Express each of the following in exponential form :

(i) $\frac{2}{3} \times \frac{2}{3} \times \frac{2}{3} \times \frac{2}{3}$

(ii) $\frac{3}{8} \times \frac{3}{8} \times \frac{3}{8} \times \frac{3}{8} \times \frac{3}{8}$

(iii) $\frac{-5}{7} \times \frac{-5}{7} \times \frac{-5}{7} \times \frac{-5}{7} \times \frac{-5}{7} \times \frac{-5}{7}$


Q2 | Ex-2A | Exponents |Class 8 | Schand composite mathematics| Chapter 2 | myhelper

Question 2

2. Express each of the following as a rational number of the form $\frac{p}{q}$ :

(i) $\left(\frac{5}{9}\right)^{2}$

(ii) $\left(\frac{4}{7}\right)^{3}$

(iii) $\left(\frac{-2}{3}\right)^{7}$

(iv) $\left(\frac{-5}{2}\right)^{3}$

$(v)\left(\frac{-1}{2}\right)^{8}$


Q3 | Ex-2A | Exponents |Class 8 | Schand composite mathematics| Chapter 2 | myhelper

3. Express each of the following rational numbers in power notation :

(i) $\frac{9}{64}$

(ii) $\frac{49}{25}$

(iii) $\frac{-8}{27}$

(iv) $-\frac{1}{216}$

(v) $\frac{-32}{243}$

(vi) $\frac{81}{625}$



Q4 | Ex-2A | Exponents |Class 8 | Schand composite mathematics| Chapter 2 | myhelper

4. Find the value of :

(i) $\left(\frac{1}{3}\right)^{3} \times\left(\frac{3}{2}\right)^{2}$

(ii) $\left(\frac{-2}{3}\right)^{4} \times\left(\frac{-3}{4}\right)^{3}$

(iii) $\left(-\frac{1}{5}\right)^{3} \times\left(-\frac{1}{5}\right)^{2}$

(iv) $\left(\frac{4}{-5}\right)^{2} \times(-5)^{3}$

(v) $\left(-\frac{1}{3}\right)^{5} \div\left(\frac{2}{3}\right)^{3}$

(vi) $\left(-\frac{1}{5}\right)^{3} \times(-1)^{85} \times\left(\frac{2}{5}\right)^{2}$

(vii) $\left(\left(\frac{-3}{5}\right)^{3}+\frac{7}{25}\right) \div\left(\frac{5}{2}\right)^{3}$


Q5 | Ex-2A | Exponents |Class 8 | Schand composite mathematics| Chapter 2 | myhelper

5. Find the reciprocal of :

(i) $\frac{16}{125}$

(ii) $\frac{-27}{64}$

(iii) $(-2)^{4}$

(iv) $\left(\frac{-3}{7}\right)^{2}$


Q6 | Ex-2A | Exponents |Class 8 | Schand composite mathematics| Chapter 2 | myhelper

OPEN IN YOUTUBE

6. Evaluate : $b^{2}-9(b-1)^{2}$, if b=1.1.



Multiple Choice Questions (MCQs)

Q7 | Ex-2A | Exponents |Class 8 | Schand composite mathematics| Chapter 2 | myhelper

7. $\left(12^{2}-5^{3}\right) \times \frac{(-1)^{20}}{19}$ equals

(a) 0

(b) 1

(c) $-1$

(d) 2


Q8 | Ex-2A | Exponents |Class 8 | Schand composite mathematics| Chapter 2 | myhelper

8. The multiplicative inverse of $\left(\frac{1}{2}\right)^{4} \div\left(\frac{1}{3}\right)^{4}+\left(-\frac{1}{2}\right)^{3}$ is

(a) $\frac{79}{17}$

(b) $-\frac{79}{16}$

(c) $\frac{16}{79}$

(d) $-\frac{17}{79}$


High Order Thinking Skills (HOTS)

Q9 | Ex-2A | Exponents |Class 8 | Schand composite mathematics| Chapter 2 | myhelper

9. Find the reciprocal of $\frac{-1296}{625}$ and express it in exponential notation.





























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S.chand publication New Learning Composite mathematics solution of class 8 Chapter 2 Exponents Exercise 2B

 Exercise 2B

Q1 | Ex-2A |Class 8 |Exponents | S.Chand | New Learning | Composite maths | Chapter 2 | myhelper

Question 1

Find each value

(a) 10-4

Sol : 

$=\frac{1}{(10)^4}=\frac{1}{10000}$


(b) 10-7

Sol : 

$=\frac{1}{(10)^7}=\frac{1}{10000000}$


(c) 10-8

Sol :

$=\frac{1}{100000000}$

(d) 10-10

Sol : 

$=\frac{1}{10000000000}$


Q2 | Ex-2A |Class 8 |Exponents | S.Chand | New Learning | Composite maths | Chapter 2 | myhelper

Question 2

Write each number in scientific notation.

(a) 5,700,000

Sol : 

=57×105

=5.7×106


(b) 8,19,000

Sol :

=819×103

=8.19×105


(c) 4,000,000,000

Sol :

=4×10-9


(d) 56,000

Sol :

=56×103

=5.6×104


Q3 | Ex-2A |Class 8 |Exponents | S.Chand | New Learning | Composite maths | Chapter 2 | myhelper

Question 3

(a) 0.000053

Sol :

=53×10-6

=5.3×10-5


(b) 0.000000084

Sol :

=8.4×10-9

=8.4×10-8


(c) 0.0009

Sol :

=9×10-4


(d) 0.0603

Sol :

=603×10-4

=6.03×10-2


Q4 | Ex-2A |Class 8 |Exponents | S.Chand | New Learning | Composite maths | Chapter 2 | myhelper

Question 4

Write each number in standard form.

(a) 5.7 x 103

Sol :

$=\frac{57 \times 1000}{10}$

=5700


(b) 6.39 x 105

Sol :

$=\frac{639 \times 100000}{100}$

=639000


(c) 1.71 x 106

Sol :

$=\frac{171 \times {10}^6}{{10}^2}$

=1710000


(d) 4.0 x 109

Sol :

$=4 \times {10}^{9}$

=4000000000


(e) 7.02 × 104

Sol :

$=\frac{702 \times 10^4}{10^2}$

=70200


Q5 | Ex-2A |Class 8 |Exponents | S.Chand | New Learning | Composite maths | Chapter 2 | myhelper

Question 5

(a) 9.4 x 10-4

Sol : 

$=\frac{94\times 10^{-4}}{10}$

=0.00094


(b) 2 x 10-3

Sol : 

$=\frac{2}{1000}$

=0.002


(c) 5.01 x 10-2

Sol : 

$=\frac{501\times 10^{-2}}{100}$

=0.0501


(d) 3.88 x 10-1

Sol : 

$=\frac{388\times 10^{-1}}{10^2}$

=0.388


(e) 3.7×10-9

Sol : 

$=\frac{37\times 10^{-9}}{10}$

=0.0000000037


Q6 | Ex-2A |Class 8 |Exponents | S.Chand | New Learning | Composite maths | Chapter 2 | myhelper

Question 6

Write the following facts in scientific notation.

(a) The distance from the earth to the sun is 149600000000 m.

Sol : 1.496×1011 m

(b) the average diameter of a red blood cell is 0.000007 mm.

Sol : 7×10-6 mm

(c) Diameter of a wire in a computer chip is 0.000003 m.

Sol : 3×10-6 m

(d) Size of a plant cell is 0.00001275 m.

Sol : 1.275×10-5 m

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S.chand publication New Learning Composite mathematics solution of class 8 Chapter 2 Exponents Exercise 2A

 Exercise 2A

Q1 | Ex-2A |Class 8 |Exponents | S.Chand | New Learning | Composite maths | myhelper

Question 1

Evaluate

(a) 90

Sol : 1


(b) $\left(\frac{1}{3}\right)^0$

Sol : 1


(c) $\left(-\frac{64}{21}\right)^0$

Sol : 1


(d) (395.008)0

Sol : 1


(e) $\left(\frac{3xy}{ab}-z\right)^0$

Sol : 1


(f) $\frac{1}{a^0 + b^0 + c^0}$

Sol : $=\frac{1}{3}$

(g) (80 – 20)x 250

Sol : 

=(1-1)×1

=0×1=0


(h) (350 + 20 + 30) ÷ 3

Sol : 1


Q2 | Ex-2A |Class 8 |Exponents | S.Chand | New Learning | Composite maths | myhelper

Question 2

Simplifying giving the answer as a fraction:
(a) 6-1

Sol : $=\frac{1}{6}$

(b) 10-1

Sol : $=\frac{1}{10}$

(c) 4-3

Sol : $=\frac{1}{4^3}=\frac{1}{64}$


(d) 2-7

Sol : 
$=\frac{1}{2^7}=\frac{1}{128}$


(e) 3-3

Sol : 
$=\frac{1}{3^3}=\frac{1}{27}$


(f) p-1

Sol : 
$=\frac{1}{p}$


(g) (x-2)2

Sol : 
$=\frac{1}{x^4}$


(h) (10a)-2

Sol : 
$=\frac{1}{100a^2}$


(i) (x+y)-2

Sol : 
$=\frac{1}{(x+y)^2}$


(j) (m5)-3

Sol : 
$=\frac{1}{m^{15}}$


Q3 | Ex-2A |Class 8 |Exponents | S.Chand | New Learning | Composite maths | myhelper

Question 3

Find the reciprocal of the following.

(a) (3)-2

Sol : 
$=\frac{1}{3^2}=\frac{1}{9}$


(b) (-2)-5

Sol : 
$=\frac{1}{(-2)^5}=-\frac{1}{32}$


(c) $\left(\frac{2}{5}\right)^{-3}$
Sol : 

$=\left(\frac{5}{2}\right)^3=\frac{125}{8}$


(d) $\left(\frac{2}{3}\right)^{-4}$

Sol : 

$=\left(\frac{3}{2}\right)^4=\frac{81}{16}$


Q4 | Ex-2A |Class 8 |Exponents | S.Chand | New Learning | Composite maths | myhelper

Question 4

Simplify and express the result in power notation with positive exponent.
(a) (-2)-4 x (-2)-6

Sol : $=\frac{1}{-2^4}\times \frac{1}{-2^6}=\frac{1}{2^{10}}$

(b) 37 x 3-9 x 36

Sol : $=\frac{1}{3^7}\times \frac{1}{3^9}\times \frac{1}{3^{6}}$
=34

(c) $3^7\times \left(\frac{3}{5}\right)^{-7}$

Sol : $=3^7 \times \left(\frac{5}{3}\right)^7=3^7 \times  \frac{5^7}{3^{7}}$

=57

(d) 2-7 x [(2)-3]-4

Sol : $=\frac{1}{2^7}\times 2^{12}$

=25

(f) (4-8 ÷ 4-10) x 4-5

Sol : $=\frac{4^{-8}}{4^{-10}}\times 4^{-5}$ $=\frac{1}{4^2}\times 4^{-5}=4^{-3}=\frac{1}{4^3}$


Q5 | Ex-2A |Class 8 |Exponents | S.Chand | New Learning | Composite maths | myhelper

Question 5

Evaluate:
(a) (80 + 5-1)×$\left(\frac{1}{5}\right)^{-2}$

Sol :

$=\left(1+\frac{1}{5}\right)\times (5^{-1})^{-2}$

$=\frac{5+1}{5}\times 5^2$

$=\frac{6}{5}\times 5^2$

=6×5=30


(b) (300+ 150)×$\left(\frac{1}{2}\right)^{-3}$

Sol :

=(1+1)×(2-1)-3=2×23

=24=16


(c) (7 -1+ 8-1 + 9-1)0÷$\left(-\frac{1}{9}\right)^{-2}$

Sol :

$=\left(\frac{1}{7}+\frac{1}{8}+\frac{1}{9}\right)^0 \div \left(\frac{9}{-1}\right)^2$
$=1\div \frac{81}{1}=\frac{1}{81}$

(d) $\left[\left(\frac{1}{3}\right)^{-2}+\left(\frac{1}{4}\right)^{-2}+\left(\frac{1}{6}\right)^{-2}\right]$

Sol :

=32+42+62

=9+16+36

=25+36=61


(e) $\left\{\left(-\frac{4}{5}\right)^{-2}\right\}^{-2}$

Sol :

$=\left\{\left(-\frac{5}{4}\right)\right\}^{-2}=\left(-\frac{5}{4}\right)^{-4}$

$=\left(\frac{4}{5}\right)^4=\frac{256}{625}$


(f) $9^{-1}\times \frac{4^3}{3^{-4}}$

Sol :

$=\frac{(3^2)^{-1}\times 4^3}{3^{-4}}=\frac{3^{-2}\times 4^3}{3^{-4}}$

$=\frac{4^3}{3^{-2}}$

=43×32=576


(g) $(5^{-1}\times 4^{-1})\times \left(\frac{3}{2}\right)^{-2}$

Sol :

$=\left(\frac{1}{5}\times \frac{1}{4}\right)\times \left(\frac{2}{3}\right)^2$

$=\frac{1}{20}\times \frac{2^2}{3^2}$

$=\frac{1}{20}\times \frac{4}{9}=\frac{1}{45}$


Q6 | Ex-2A |Class 8 |Exponents | S.Chand | New Learning | Composite maths | myhelper

Question 6

Evaluate:

(a) $\left[\left(\frac{1}{4}\right)^{-1}-\left(\frac{1}{5}\right)^{-1}\right]+1$
Sol :

=(4-5)+1

=-1+1=0


(b) $\left[\left(\frac{11}{12}\right)^{-10} \div \left(\frac{11}{12}\right)^{-12}\right]\times 1\frac{23}{121}$

Sol :

$=\left[\left(\frac{12}{11}\right)^{10}\div \left(\frac{12}{11}\right)^{12}\right]\times \frac{144}{121}$

$=\left(\frac{12}{11}\right)^{-2}\times \left(\frac{12}{11}\right)^{2}$

$=\frac{(11)^2}{(12)^2}\times \frac{(12)^2}{(11)^2}$

=1


Q7 | Ex-2A |Class 8 |Exponents | S.Chand | New Learning | Composite maths | myhelper

Question 7

Find the value of m for which, 72m ÷ 7-4 = 7-6

Sol :

$=\frac{7^{2m}}{7^{-4}}=$7-6

⇒72m=7-6×7-4=7-10

⇒(72)m=(72)-5

⇒m=-5

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RS Aggarwal solution class 8 chapter 2 Exponents Test Paper 2

Test Paper 2

Page-39

Q1 Test Paper 2 Class 8 RS AGGARWAL chapter 2 Exponents Solution

Question 1:

Evaluate:
(i) 3−4
(ii) (−4)3
(iii) 34-2
(iv) -23-5
(v) 570

Answer 1:

(i) 3-4=134=181

(ii) -43=-13×43=-1×64=-64

(iii) 34-2=432=4232=169

(iv) -23-5=3-25=35-25=243-32=243×-1-32×-1=-24332

(v) Using the property ab0=1, we have:
570 = 1


Q2 Test Paper 2 Class 8 RS AGGARWAL chapter 2 Exponents Solution

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Question 2:

Evaluate: -233-2.

Answer 2:

-233-2=-23-6=3-26=36-26=72964


Q3 Test Paper 2 Class 8 RS AGGARWAL chapter 2 Exponents Solution

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Question 3:

Simplify: (3-1+6-1)÷34-1.

Answer 3:

3-1+6-1÷34-1=13+16÷431=1×23×2+1×16×1÷43=2+16÷43=36÷43=12÷43=12×34=38

∴ 3-1+6-1÷34-1=38


Q4 Test Paper 2 Class 8 RS AGGARWAL chapter 2 Exponents Solution

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Question 4:

By what number should -23-3 be divided so that the quotient is 49-2?

Answer 4:

Let the number be x.

∴$\left(\frac{-2}{3}\right)^{-3} \div x=\left(\frac{4}{9}\right)^{-2}$

$\Rightarrow\left(\frac{3}{-2}\right)^{3}+x=\left(\frac{9}{4}\right)^{2}$

$\Rightarrow \frac{\left(\frac{3}{-2}\right)^{3}}{x}=\left(\frac{9}{4}\right)^{2}$

$\Rightarrow \frac{3^{3}}{-2^{3}}=\frac{9^{2}}{4^{2}}$

$\Rightarrow x=\frac{\left(\frac{3^{3}}{-2^{3}}\right)}{\left(\frac{9^{2}}{4^{2}}\right)}=\frac{\left(\frac{3^{3}}{-2^{3}}\right)}{\left(\frac{\left(3^{2}\right)^{2}}{\left(2^{2}\right)^{2}}\right)}$

$=\left(\frac{3^{3}}{-2^{3}}\right) \times\left(\frac{\left(2^{2}\right)^{2}}{\left(3^{2}\right)^{2}}\right)$

$=\left(\frac{3^{3}}{-2^{3}}\right) \times\left(\frac{2^{4}}{3^{4}}\right)$

$=\left(\frac{3^{3}}{-2^{3}}\right) \times\left(\frac{2^{3}}{3^{3}}\right) \times\left(\frac{2^{1}}{3^{1}}\right)$


$\Rightarrow\left(\frac{1}{-1}\right) \times\left(\frac{2^{1}}{3^{1}}\right)=\frac{2}{-3}=\frac{2 \times-1}{-3 \times-1}=\frac{-2}{3}$


Q5 Test Paper 2 Class 8 RS AGGARWAL chapter 2 Exponents Solution

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Question 5:

By what number should (−3)−1 be multiplied so that the product becomes 6−1?

Answer 5:

Let the number be x.

∴ -3-1×x=6-1
⇒1-3 × x=16⇒ 1 × -1-3 × -1 × x=16∴ -x3 = 16On cross multiplying:-x × 6 = 1 × 3⇒-6x = 3⇒6x = -3∴ x = -36 = -12


Q6 Test Paper 2 Class 8 RS AGGARWAL chapter 2 Exponents Solution

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Question 6:

Express each of the following in standard form:
(i) 345
(ii) 180000
(iii) 0.000003
(iv) 0.000027

Answer 6:

(i) 345=3.45×100$=3.45 \times 10^{2}$

(ii) 180000=18×10000$=18 \times 10^{4}=1.8 \times 10 \times 10^{4}$
$=1.8 \times 10^{(1+4)}=1.8 \times 10^{5}$

(iii) 0.000003$=\frac{3}{1000000}=3 \times 10^{-6}$

(iv) 0.000027$=\frac{27}{100000}=\frac{27}{10^{6}}$

$=\frac{2.7 \times 10}{10^{6}}$

$=2.7 \times 10^{(1-6)}$

$=2.7 \times 10^{-5}$


Q7 Test Paper 2 Class 8 RS AGGARWAL chapter 2 Exponents Solution

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Question 7:

Mark (✓) against the correct answer
The value of (−3)−3 is
(a) −27
(b) 9
(c) -127
(d) 127

Answer 7:

(c) -127

-3-3=1-33=13-33=1-27=1×-1-27×-1=-127


Q8 Test Paper 2 Class 8 RS AGGARWAL chapter 2 Exponents Solution

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Question 8:

Mark (✓) against the correct answer
The value of 34-3 is
(a) -2764
(b) 6427
(c) -94
(d) 2764

Answer 8:

(b) 6427

34-3=433=4333=6427


Q9 Test Paper 2 Class 8 RS AGGARWAL chapter 2 Exponents Solution

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Question 9:

Mark (✓) against the correct answer
(3−6 ÷ 34) = ?
(a) 3−2
(b) 32
(c) 3−10
(d) 310

Answer 9:

(c) 3-10

3-6÷34=136÷34=136×134=136+4=1310=3-10


Q10 Test Paper 2 Class 8 RS AGGARWAL chapter 2 Exponents Solution

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Question 10:

Mark (✓) against the correct answer
If 512-4×5123x=5125, then x=?
(a) −1
(b) 1
(c) 2
(d) 3

Answer 10:

(d) 3

512-4×5123x=5125⇒512-4+3x=5125⇒ -4+3x=5⇒3x=5+4=9⇒x=93=3


Q11 Test Paper 2 Class 8 RS AGGARWAL chapter 2 Exponents Solution

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Question 11:

Mark (✓) against the correct answer
350=?
(a) 53
(b) 35
(c) 1
(d) 0

Answer 11:

(c) 1

Using the law of exponents, which says ab0=1, we get:
 350=1


Q12 Test Paper 2 Class 8 RS AGGARWAL chapter 2 Exponents Solution

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Question 12:

Mark (✓) against the correct answer
-65-1=?
(a) 65
(b) -65
(c) 56
(d) -56

Answer 12:

(d) -56

-65-1=5-61=5-6=5×-1-6×-1=-56


Q13 Test Paper 2 Class 8 RS AGGARWAL chapter 2 Exponents Solution

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Question 13:

Mark (✓) against the correct answer
-133=?
(a) -19
(b) 19
(c) -127
(d) 127

Answer 13:

(c) -127

-133=-1333=-127


Page-40


Q14 Test Paper 2 Class 8 RS AGGARWAL chapter 2 Exponents Solution

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Question 14:

Fill in the blanks.
(i) 360000 written in standard form is .........
(ii) 0.0000123 written in standard form is .........
(iii) -23-2=.........
(iv) 3 × 10−3 in usual form is .........
(v) 5.32 × 10−4 in usual form is .........

Answer 14:

(i) The standard form of 36000 is $3.6 \times 10^{5}$

$360000=36 \times 10^{4}=3.6 \times 10 \times 10^{4}$

$=3.6 \times 10^{(1+4)}=3.6 \times 10^{5}$

(ii) The standard form of 0.0000123 is $1.23 \times 10^{-5}$

$0.0000123=\frac{123}{10000000}=\frac{123}{10^{7}}$

$=\frac{1.23 \times 100}{10^{7}}=\frac{1.23 \times 10^{2}}{10^{7}}$

$=1.23 \times 10^{(2-7)}=1.23 \times 10^{-5}$

(iii) $\left(\frac{-2}{3}\right)^{-2}=\frac{9}{4}$
$\left(\frac{-2}{3}\right)^{-2}=\left(\frac{3}{-2}\right)^{2}=\frac{3^{2}}{-2^{2}}=\frac{9}{4}$


(iv) The usual form of $3 \times 10^{-3}$ is 0.003.
$3 \times 10^{-3}=\frac{3}{10^{3}}=\frac{3}{1000}$=0.003​

(v) The usual form of $5.32 \times 10^{-4}$ is 0.000532.
$5.32 \times 10^{-4}=\frac{5.32}{10^{4}}=\frac{5.32}{10000}$=0.000532
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