Question

Rewrite the expression with a rational exponent as a radical expression.

(4^2/5)^1/4


a.)^10sqrt4
b.)^4sqrt4
c.)^5sqrt4^2
d.)sqrt4^10


sqrt=square root

Answer 1

Answer:

First option is correct.

$\sqrt[10]{4}$

Step-by-step explanation:

Given:

The given expression is $(4^{\frac{2}{5}})^{\frac{1}{4}}$

We write the given expression with a rational exponent as a radical expression such as.

$=(4^{\frac{2}{5}})^{\frac{1}{4}}$

Simplify the above equation by multiplication of powers.

$=(4^{\frac{2}{5}\times \frac{1}{4}})$

$=(4^{\frac{1}{5}\times \frac{1}{2}})$

$=(4^{\frac{1}{5\times 2}})$

$=(4^{\frac{1}{10}})$

$=\sqrt[10]{4}$

Therefore, The answer is $=\sqrt[10]{4}$.