Question

Write the following numbers using positive indices.
(i) ${27}^{-2}$ (ii) $\frac{1}{{13}^{-5}}$ (iii) ${16}^{-3}$ (iv) $y^{-4}$

Answer 1

It is known that, $a^{-m}=\frac{1}{a^m}$ where $m$ is an integer and '$a$' is a non-zero rational number.​

(i) ${27}^{-2}=\frac{1}{{27}^2}=\frac{1}{(3^3{)}^2}=\frac{1}{3^6}$ [$\because (a^m{)}^n=a^{mn}$]

(​ii) $\frac{1}{{13}^{-5}}={13}^5$

(iii) ${16}^{-3}=\frac{1}{{16}^3}=\frac{1}{(2^4{)}^3}=\frac{1}{2^{12}}$

(iv) $y^{-4}=\frac{1}{y^4}$