Question

Pls give an explanation w your answer

Answer 1

$a^{\frac{1}{n}}=\sqrt[n]{a}\\\\\left(a^n\right)^m=a^{n\cdot m}\\\\a^n\cdot a^m=a^{n+m}$
therefore
$64^\frac{1}{4}=\left(2^6\right)^\frac{1}{4}=2^{6\cdot\frac{1}{4}}\\\\=2^\frac{6}{4}=2^{1\frac{2}{4}}=2^{1+\frac{2}{4}}=2\cdot2^\frac{2}{4}\\\\=2\sqrt[4]{2^2}=2\sqrt[4]4$
Other method:
$64^\frac{1}{4}=\sqrt[4]{64}=\sqrt[4]{16\cdot4}=\sqrt[4]{16}\cdot\sqrt[4]4=2\sqrt[4]4$


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Answer 2

For this case we have the following expression:
 64 ^ (1/4)
 Rewriting we have:
 4 ^ root (64)
 4 ^ root (2 * 2 * 2 * 2 * 4)
 For power properties we have:
 4 ^ root ((2 ^ 4) * 4)
 2 * (4 ^ root (4))
 Answer:
 2 * (4 ^ root (4))
 option 1