Answer:
Option (a) is correct.
[tex](64)^\frac{1}{4}=2\sqrt[4]{4}[/tex]
Step-by-step explanation:
Given : Expression [tex](64)^\frac{1}{4}[/tex]
We have to choose an equivalent expression to the given expression [tex](64)^\frac{1}{4}[/tex]
Consider the given expression [tex](64)^\frac{1}{4}[/tex]
64 can be written as 2 × 2 × 2 × 2 × 2× 2 =[tex]2^6[/tex]
Thus, The given expression becomes,
[tex](64)^\frac{1}{4}=(2^6)^\frac{1}{4}[/tex]
Also, [tex]2^6=2^4\cdot2^2[/tex]
Thus,
[tex](2^6)^\frac{1}{4}=(2^4\cdot 2^2)^\frac{1}{4}[/tex]
Simplify, we have,
[tex]=2\sqrt[4]{4}[/tex]
Thus, [tex](64)^\frac{1}{4}=2\sqrt[4]{4}[/tex]
