Question

Explain how to evaluate simplify and convert to radical form (x^3/8)^3/4

Answer 1

Answer:

$(x^\frac{3}{8})^\frac{3}{4} = \sqrt[32]{x^9}$

Step-by-step explanation:

Given

$(x^\frac{3}{8})^\frac{3}{4}$

Required

Convert to radical form

$(x^\frac{3}{8})^\frac{3}{4}$

Evaluate the exponents

$(x^\frac{3}{8})^\frac{3}{4} = x^\frac{3*3}{8*4}$

$(x^\frac{3}{8})^\frac{3}{4} = x^\frac{9}{32}$

Split the exponent

$(x^\frac{3}{8})^\frac{3}{4} = (x^9)^\frac{1}{32}$

Apply the following law of indices

$(x^a)^\frac{1}{b} = \sqrt[b]{x^a}$

So, we have:

$(x^\frac{3}{8})^\frac{3}{4} = \sqrt[32]{x^9}$