Question

Simplify and Show your Work

Answer 1

Step-by-step explanation:

$\sf \: {2}^{ \frac{1}{2 } } = \sqrt{2}$

$\sf \: {2}^{ \frac{2}{3} } = \sqrt[3]{ {2}^{2} }$

$\sf \: {3}^{ \frac{3}{2} } = \sqrt{ {3}^{3} }$

$\sf \: {3}^{ \frac{1}{3} } = \sqrt[3]{3}$

Answer 2

Step-by-step explanation:

$2 ^{ \frac{1}{2} } = 2 ^{1 \times \frac{1}{2} } = \sqrt{2} \\ {2}^{ \frac{2}{3} } = 2 ^{2 \times \frac{1}{3} } = \sqrt[3]{2 ^{2} } \\ 3 ^{ \frac{3}{2} } = {3}^{3 \times \frac{1}{2} } = \sqrt[]{ {3}^{3} } \\ {3}^{ \frac{1}{3} } = 3 ^{1 \times \frac{1}{3} } = \sqrt[3]{3}$