Question

Complete the steps to simplify^5√4 x √2 . Rewrite using rational exponents.

Answer 1

The answer is 2^(9/10). I did it assuming with the ^5 you mean the 5th root of 4

Answer 2

ANSWER

${2}^{ \frac{9}{10} }$

EXPLANATION

The given expression is

$\sqrt[5]{4} \times \sqrt{2}$

Recall that:

$\sqrt[n]{ {a}^{m} } = {a}^{ \frac{m}{n} }$

$\sqrt[5]{ {2}^{2} } \times \sqrt{ {2}^{1} }$

$\sqrt[5]{ {2}^{2} } \times \sqrt{ {2}^{1} } = {2}^{ \frac{2}{5} } \times {2}^{ \frac{1}{2} }$

Recall that:

${a}^{m} \times {a}^{n} = {a}^{m + n}$

We now apply this property of a exponents to obtain:

$\sqrt[5]{ {2}^{2} } \times \sqrt{2} = {2}^{ \frac{2}{5} + \frac{1}{2} } = {2}^{ \frac{9}{10} }$