Question

the value of ⁴root (16) -2: options: a. 1/4 b.1/2 c.4 d.1/16​

Answer 1

Solution -

$\sqrt[4]{(16)^{ - 2} } = \sqrt[4] { \bigg( \large\frac{1}{16} \bigg)^{2} } \\ \: \: \: \: \: \: \: \: \: \: \: \: = \sqrt[4]{ \frac{ {(1)}^{2} }{ {(16)}^{2} } } \\ \: \: \: \: = \sqrt[4] { \bigg(\frac{1}{256} \bigg)} \\ = \sqrt[4]{ \frac{1}{(2)^{ 8} } } = \sqrt[4]{ {(2)}^{ - 8} } = 4 \times |2| ^{ - 4} \\ \implies4 \times \frac {1}{16} \longrightarrow \rm\red { reduce \: the \: number \: with \: GCF \: 4} \\ \rm { Now,} \\ \implies\cancel4 \times \frac {1}{ \cancel{16}_{4}}= \red{\frac {1}{4}}$

So, option 1️⃣ 1/4 [ Answer ]

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