Question

Select the simplification that accurately explains that following statement

Answer 1

The correct answer is D

Answer 2

(D)
`(7^{(1)/(3)})^3=7`

Explanation:

The following statement is:

`\sqrt[3]{7}=7^{(1)/(3)}`

Now,
`(7^{(1)/(3)})^3=7^{(1)/(3)}\cdot7^{(1)/(3)}\cdot7^{(1)/(3)}`

Using, the power and exponents properties that is
`a^a{\cdot}a^b=a^(a+b)`, we get

`(7^{(1)/(3)})^3=7^{(1)/(3)+(1)/(3)+(1)/(3)}`

`(7^{(1)/(3)})^3=7^{(3)/(3)}`

`(7^{(1)/(3)})^3=7^1`

`(7^{(1)/(3)})^3=7`

Thus, option D is correct.