Question

Determine whether each expression is equivalent to (8n2)25. Select Yes or No for each expression.

Answer 1

Simplify first

$\\ \tt\longmapsto (8n^2)^{\frac{2}{5}}=8n^{\frac{4}{5}}$

#1

$\\ \tt\longmapsto \sqrt[5]{8n^4}$

$\\ \tt\longmapsto 8n^{4/5}$

• Yes

#2

$\\ \tt\longmapsto \sqrt[5]{64n^2}=\sqrt[5]{(8n)^2}$

$\\ \tt\longmapsto 8n^{2/5}$

• No

#3

$\\ \tt\longmapsto 2\sqrt[5]{2n^4}=4n^{4/5}$

• No

#4

$\\ \tt\longmapsto \sqrt[5]{64n^4}$

• No