Question

The value of $\sqrt[4]{4(64{)}^{-2}}$ is :

• A. $\frac{1}{8}$
• B. $\frac{1}{2}$
• C. 8
• D. $\frac{1}{64}$

Answer 1

The correct option is A $\frac{1}{8}$

$\Rightarrow$ $\sqrt[4]{4(64{)}^{-2}}$

$\Rightarrow$ $\sqrt[4]{4\frac{1}{{64}^2}}$ $[\because x^{-n}=\frac{1}{x^n}]$

$\Rightarrow$ $\sqrt[4]{4\frac{1}{(8^2{)}^2}}$

$\Rightarrow$ $\sqrt[4]{4\frac{1}{8^4}}$

$\Rightarrow$ $\frac{1}{8}$

$\therefore$ $\sqrt[4]{4(64{)}^{-2}}=\frac{1}{8}$