Question

Solve: with full workings (32/243)^-4/5​

Answer 1

Answer:

$(\frac{32}{243})^{-\frac{4}{5}}=39.0625$

Step-by-step explanation:

Given

$(\frac{32}{243})^{-\frac{4}{5}}$

Required

Solve

$(\frac{32}{243})^{-\frac{4}{5}}$

Express 32 as 2^5 and 243 as 3^5

$(\frac{2^5}{3^5})^{-\frac{4}{5}}$

The exponent can be expressed as 1\5 * -4

So we have:

$(\frac{2^5}{3^5})^{\frac{1}{5} * -4}$

Apply law of indices:

$(\frac{2^{5*1/5}}{5^{5*1/5}})^{-4}$

$(\frac{2}{5})^{-4}$

In indices:

$(\frac{a}{b})^{-c} = (\frac{b}{a})^{c}$

So, the expression becomes

$(\frac{5}{2})^{4}$

$(\frac{5^{4}}{2^{4}})$

$\frac{625}{16}$

$39.0625$

Hence:

$(\frac{32}{243})^{-\frac{4}{5}}=39.0625$