Question

State TRUE or FALSE.
$(32{)}^{-\frac{2}{5}}÷(125{)}^{-\frac{2}{3}}$ is equal to $6\frac{1}{4}$

• A. True
• B. False

Answer 1

The correct option is A True

As given
$\Rightarrow (32{)}^{-\frac{2}{5}}÷(125{)}^{-\frac{2}{3}}$

$\Rightarrow \frac{1}{{\left(2^5\right)}^{\frac{2}{5}}}÷\frac{1}{{\left(5^3\right)}^{\frac{2}{3}}}$

$\Rightarrow \frac{1}{2^{5.\frac{2}{5}}}÷\frac{1}{5^{3.\frac{2}{3}}}$

$\Rightarrow \frac{1}{2^2}÷\frac{1}{5^2}$

$\Rightarrow \frac{1}{4}\times 25$

$\Rightarrow 6\frac{1}{4}$