Question

Find the multiplicative inverse

Please send the appropriate answer then I will brainlist your answer​​

Answer 1

Answer:

Step-by-step explanation:

Question:-

$\bigg( \frac{81}{16} \bigg)^{ \frac{ - 3}{4} }$

To find:-

The multiplicative inverse .

Solution:-

Let's solve the problem

we have,

$\bigg( \frac{81}{16} \bigg)^{ \frac{ - 3}{4} }$

$⟹ \bigg( \frac{ {3}^{4} }{ {2}^{4} } \bigg) ^{ \frac{ - 3}{4} }$

$⟹\left[ \bigg( \frac{3}{2} \bigg) ^{4} \right] ^{ \frac{ - 3}{4} }$

$⟹ \bigg( \frac{3}{2} \bigg) ^{ (\frac{ - 3}{ \cancel{4}}) \times \cancel{4}}$

$⟹ \bigg( \frac{3}{2} \bigg) ^{ - 3}$

$⟹ \bigg( \frac{2}{3} \bigg) ^{3}$

$⟹ \frac{ {2}^{3} }{ {3}^{3} }$

$⟹ \frac{2 \times 2 \times 2}{3 \times 3 \times 3}$

$⟹\frac{8}{27}$

Answer:-

$\mathrm{The \: multiplicative \: inverse \: of \bigg( \frac{81}{16} \bigg)^{ \frac{ - 3}{4} } is} \: \frac{8}{27}$

:)