Question

The value of 4 dived (81)-2

Answer 1

Step-by-step explanation:

$\bf \underline{Solution-}$

$\bf{ \sqrt[4]{(81 {)}^{ - 2} } }$

$\bf = \sqrt[4]{ \bigg( \frac{1}{81} \bigg) ^{2} }$

$\bf = \sqrt[4] {\left\{{ \bigg( \frac{1}{9} \bigg) ^{2} }\right\} ^{2} }$

$\bf = \sqrt[4]{ \bigg( \frac{1}{9} \bigg) ^{4} }$

$\bf = \bigg( \frac{1}{9} \bigg) ^{4 \times \frac{1}{4} }$

$\bf = \frac{1}{9} \:$

$\bf \underline{Hence \: the \: value \: of \: \sqrt[4]{(81 {)}^{ - 2} } } \: is \: \frac{1}{9} .$