Question

Simplified value of ${\left(16\right)}^{-\frac{1}{4}}\times \sqrt[4]{16}$ is
(a) 0
(b) 1
(c) 4
(d) 16

Answer 1

$$\begin{gathered} {\left(16\right)}^{-\frac{1}{4}}\times \sqrt[4]{16}={\left(2^4\right)}^{-\frac{1}{4}}\times {\left(2^4\right)}^{\frac{1}{4}} \\ ={\left(2\right)}^{-1}\times {\left(2\right)}^1 \\ =2^{-1+1} \\ =2^0 \\ =1 \end{gathered}$$

$\therefore$Simplified value of ${\left(16\right)}^{-\frac{1}{4}}\times \sqrt[4]{16}$ is 1.

Hence, the correct option is (b).