MCQ
The simplified form of $16^{\frac{-1}{4}}\times\sqrt[4]{16}$ is:
- ✓$1$
- B$6$
- C$4$
- D$16$
✓
Answer
Correct option: A.
$1$
$16^{\frac{-1}{4}}\times\sqrt[4]{16}$
But, $16=2^4$
So,
$\Rightarrow16^{\frac{-1}{4}}\times\sqrt[4]{16}$
$\Rightarrow\{(2)^4\}^{\frac{-1}{4}}\times(2)^{4\times\frac{1}{4}}$
$\Rightarrow(2)^{4\times\frac{-1}{2}}\times2$
$\Rightarrow2^{-1}\times2$
$\Rightarrow\frac{2}{2}$
$\Rightarrow1$
But, $16=2^4$
So,
$\Rightarrow16^{\frac{-1}{4}}\times\sqrt[4]{16}$
$\Rightarrow\{(2)^4\}^{\frac{-1}{4}}\times(2)^{4\times\frac{1}{4}}$
$\Rightarrow(2)^{4\times\frac{-1}{2}}\times2$
$\Rightarrow2^{-1}\times2$
$\Rightarrow\frac{2}{2}$
$\Rightarrow1$
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