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

 Exercise 2B

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

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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 :

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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 :

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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 :

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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 :

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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 :

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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 :

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Question 7

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

Sol :

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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 :

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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 :

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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 :

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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 :

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Question 12

Write the following numbers in scientific notation :

(i) 0.00002

(ii) 0.00000542

(iii) 0.000000093

(iv) 0.003142

Sol :

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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 :

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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)

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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 :

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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 :

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Question 17

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

(a) 2

(b) -2

(c) 7

(d) -7

Sol :

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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 :

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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)

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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 :