Question

Question 19
The value of $\sqrt[4]{4(81{)}^{-2}}$ is

A) $\frac{1}{9}$
B) $\frac{1}{3}$
C) $9$
D) $\frac{1}{81}$

Answer 1

The answer is A.
$\sqrt[4]{4(81{)}^{-2}}=\sqrt[4]{4\frac{1}{(81{)}^2}}=\frac{1}{(81{)}^{2/4}}=\frac{1}{(81{)}^{1/2}}[\because \sqrt[m]{m{a}^n}=a^{n/m}]=\frac{1}{(9^2{)}^{1/2}}=\frac{1}{9^{2/2}}=\frac{1}{9}[\because (a^m{)}^n=a^{mn}]$