Question

Pls give an explanation w your answer

Answer 1

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

Answer 2

`a^{(1)/(n)}=\sqrt[n]{a}\\\\\left(a^n\right)^m=a^(n\cdot m)\\\\a^n\cdot a^m=a^(n+m)`
therefore

`64^(1)/(4)=\left(2^6\right)^(1)/(4)=2^{6\cdot(1)/(4)}\\\\=2^(6)/(4)=2^{1(2)/(4)}=2^{1+(2)/(4)}=2\cdot2^(2)/(4)\\\\=2\sqrt[4]{2^2}=2\sqrt[4]4`
Other method:

`64^(1)/(4)=\sqrt[4]{64}=\sqrt[4]{16\cdot4}=\sqrt[4]{16}\cdot\sqrt[4]4=2\sqrt[4]4`