Exercise 2A
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) $\frac{-5}{7} \times \frac{-5}{7} \times \frac{-5}{7} \times \frac{-5}{7} \times \frac{-5}{7} \times \frac{-5}{7}$
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) $\left(\frac{-5}{2}\right)^{3}$
$(v)\left(\frac{-1}{2}\right)^{8}$
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) $\frac{81}{625}$
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) $\left(\left(\frac{-3}{5}\right)^{3}+\frac{7}{25}\right) \div\left(\frac{5}{2}\right)^{3}$
5. Find the reciprocal of :
(i) $\frac{16}{125}$
(ii) $\frac{-27}{64}$
(iii) $(-2)^{4}$
(iv) $\left(\frac{-3}{7}\right)^{2}$
6. Evaluate : $b^{2}-9(b-1)^{2}$, if b=1.1.
Multiple Choice Questions (MCQs)
7. $\left(12^{2}-5^{3}\right) \times \frac{(-1)^{20}}{19}$ equals
(a) 0
(b) 1
(c) $-1$
(d) 2
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)
9. Find the reciprocal of $\frac{-1296}{625}$ and express it in exponential notation.
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