Mathematics: Complete the steps to simplify^5√4 x √2 . rewrite using rational exponents.

this is the wrong question tipe perperly...

Complete the steps to simplify^5√4 x √2 . rewrite

Idontreallycare16

14.01.2022

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:

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

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