Question

State True or False.

Simplify and express as positive indices:
$(\frac{32x^{-5}}{243y^{-5}}{)}^{-\frac{1}{5}}$, then answer is $\frac{3x}{2y}$.

• A. True
• B. False

Answer 1

The correct option is A True

As given $(\frac{32x^{-5}}{243y^{-5}}{)}^{-\frac{1}{5}}$
$\Rightarrow {\left(\frac{2^5{x}^{-5}}{3^5{y}^{-5}}\right)}^{-\frac{1}{5}}$
$\Rightarrow \left(\frac{2^{5\cdot -\frac{1}{5}}{x}^{-5\cdot -\frac{1}{5}}}{3^{5\cdot -\frac{1}{5}}{y}^{-5\cdot -\frac{1}{5}}}\right)$
$\Rightarrow \left(\frac{2^{-1}{x}^1}{3^{-1}{y}^1}\right)$
$\Rightarrow \frac{3x}{2y}$