Exercise 2B
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 :
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 :
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 :
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 :
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 :
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 :
Question 7
If $3^{2 x+1} \div 9=27$, find x,
Sol :
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 :
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 :
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 :
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 :
Question 12
Write the following numbers in scientific notation :
(i) 0.00002
(ii) 0.00000542
(iii) 0.000000093
(iv) 0.003142
Sol :
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 :
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)
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 :
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 :
Question 17
Solve for $x: 81^{-2} \div 729^{1-x}=9^{2 x}$
(a) 2
(b) -2
(c) 7
(d) -7
Sol :
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 :
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)
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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