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} }](https://tex.z-dn.net/?f=%20%5Csqrt%5B7%5D%7B%20x%5E%7B5%7D%20%7D%20)
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} }](https://tex.z-dn.net/?f=%20%5Csqrt%5B7%5D%7B%20x%5E%7B5%7D%20%7D%20%2A%20%20%5Csqrt%5B7%5D%7B%20x%5E%7B5%7D%20%7D%20%3D%20%5C%5C%20%3D%20%5Csqrt%5B7%5D%7B%20x%5E%7B5%7D%20%2A%20x%5E%7B5%7D%20%7D%3D%20%5C%5C%20%3D%20%5Csqrt%5B7%5D%7B%20x%5E%7B10%7D%20%7D%3D%20%5Csqrt%5B7%5D%7B%20x%5E%7B7%7D%20%7D%2A%20%5Csqrt%5B7%5D%7B%20x%5E%7B3%7D%20%7D%3Dx%2A%20%5Csqrt%5B7%5D%7B%20x%5E%7B3%7D%20%7D%20%20%20%20%20)
Answer: D ) x times the seventh root of x cubed.
And the seventh root of x to the fifth power is:
Therefore:
Answer: D ) x times the seventh root of x cubed.