Question

How to simplify (32÷243)-⅕​

Answer 1

$</p><p></p><p>\begin{gathered}5 \times \frac{500}{5} \\ \\ \to \: \cancel5 \times \frac{500}{ \cancel5} \\ \\ \to \: 500\end{gathered}5×5500→5×5500→500</p><p></p><p>$

Answer 2

To simplify:-

$(\frac{32}{243})^{-\frac{1}{5}}$

Simplification:-

$(\frac{32}{243})^{-\frac{1}{5}} = (\frac{243}{32})^{\frac{1}{5}}$  $($∵ $(\frac{b}{a})^{-m} = (\frac{a}{b})^m)$

⇒ $(\frac{3^5}{2^5})^\frac{1}{5}$ $($∵ $3^5=243, 2^5=32)$

⇒ $[(\frac{3}{2})^5]^\frac{1}{5}$

⇒ $\frac{3}{2}^{5\times\frac{1}{5}$ $($∵ $(a^m)^n=a^{mn})$

⇒ $\frac{3}{2}$

⇒ $1.5$

∴ $\boxed{(\frac{32}{243})^{-\frac{1}{5}}=1.5}$