Answer:
[tex](x^\frac{3}{8})^\frac{3}{4} = \sqrt[32]{x^9}[/tex]
Step-by-step explanation:
Given
[tex](x^\frac{3}{8})^\frac{3}{4}[/tex]
Required
Convert to radical form
[tex](x^\frac{3}{8})^\frac{3}{4}[/tex]
Evaluate the exponents
[tex](x^\frac{3}{8})^\frac{3}{4} = x^\frac{3*3}{8*4}[/tex]
[tex](x^\frac{3}{8})^\frac{3}{4} = x^\frac{9}{32}[/tex]
Split the exponent
[tex](x^\frac{3}{8})^\frac{3}{4} = (x^9)^\frac{1}{32}[/tex]
Apply the following law of indices
[tex](x^a)^\frac{1}{b} = \sqrt[b]{x^a}[/tex]
So, we have:
[tex](x^\frac{3}{8})^\frac{3}{4} = \sqrt[32]{x^9}[/tex]
