Question

Simplified value of $(16{)}^{\frac{-1}{4}}\times \sqrt[4]{416}$ is :

• A. 16
• B. 4
• C. 1
• D. 0

Answer 1

Answer: (C)

1

$\Rightarrow$ $(16{)}^{\frac{-1}{4}}\times \sqrt[4]{416}$

$\Rightarrow$ $(16{)}^{\frac{-1}{4}}\times (16{)}^{\frac{1}{4}}$ $[\because x^m.x^n=x^{m+n}]$

$\Rightarrow$ $(16{)}^{\frac{-1}{4}+\frac{1}{4}}$

$\Rightarrow$ $(16{)}^0$

$\Rightarrow$ $1$ $[\because x^0=1]$

$\therefore$ $(16{)}^{\frac{-1}{4}}\times \sqrt[4]{416}=1$