Question

What is the simplified form of the seventh root of x to the fifth power times the seventh root of x to the fifth power? the square root of x x to the four ninth power x x times the seventh root of x cubed?

Answer 1

x times the seventh root of x cubed.

Explanation:

We know that x^m * x^n = x^( m + n ).

And the seventh root of x to the fifth power is: \sqrt[7]{ x^{5} }

Therefore:

\sqrt[7]{ x^{5} } * \sqrt[7]{ x^{5} } = \\ = \sqrt[7]{ x^{5} * x^{5} }= \\ = \sqrt[7]{ x^{10} }= \sqrt[7]{ x^{7} }* \sqrt[7]{ x^{3} }=x* \sqrt[7]{ x^{3} }

Answer 2

We know that x^m * x^n = x^( m + n ).
And the seventh root of x to the fifth power is:
`\sqrt[7]{ x^(5) }`
Therefore:

`\sqrt[7]{ x^(5) } * \sqrt[7]{ x^(5) } = \\ = \sqrt[7]{ x^(5) * x^(5) }= \\ = \sqrt[7]{ x^(10) }= \sqrt[7]{ x^(7) }* \sqrt[7]{ x^(3) }=x* \sqrt[7]{ x^(3) }`
Answer: D ) x times the seventh root of x cubed.