Question

State True or False.

Simplifying and expressing as positive indices $(a^{-2}b{)}^{\frac{1}{2}}\times (a{b}^{-3}{)}^{\frac{1}{3}}$, we get $\frac{1}{a^{\frac{2}{3}}{b}^{\frac{1}{2}}}$.

• A. True
• B. False

Answer 1

The correct option is A True

As given $(a^{-2}b{)}^{\frac{1}{2}}\times (a{b}^{-3}{)}^{\frac{1}{3}}$

For simplification we can write as:
$\Rightarrow \left(a^{-2\cdot \frac{1}{2}}{b}^{\frac{1}{2}}\right)\times \left(a^{\frac{1}{3}}{b}^{-3\cdot \frac{1}{3}}\right)$

$\Rightarrow \left(a^{-1}{b}^{\frac{1}{2}}\right)\times \left(a^{\frac{1}{3}}{b}^{-1}\right)$

$\Rightarrow a^{(-1+\frac{1}{3})}{b}^{(\frac{1}{2}-1)}$

$\Rightarrow a^{-\frac{2}{3}}{b}^{-\frac{1}{2}}$

$\Rightarrow \frac{1}{a^{\frac{2}{3}}{b}^{\frac{1}{2}}}$