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

`{2}^{ (9)/(10) }`

Step-by-step explanation

The given expression is

`\sqrt[5]{4} * √(2)`

Recall that:

`\sqrt[n]{ {a}^(m) } = {a}^{ (m)/(n) }`

`\sqrt[5]{ {2}^(2) } * \sqrt{ {2}^(1) }`

`\sqrt[5]{ {2}^(2) } * \sqrt{ {2}^(1) } = {2}^{ (2)/(5) } * {2}^{ (1)/(2) }`

Recall that:

`{a}^(m) * {a}^(n) = {a}^(m + n)`

We now apply this property of a exponents to obtain:

`\sqrt[5]{ {2}^(2) } * √(2) = {2}^{ (2)/(5) + (1)/(2) } = {2}^{ (9)/(10) }`