If x is positive, is \sqrt{ \frac{1}{ { {x} }^(2) } } greater than, less than, or equal to \sqrt[3]{ \frac{1}{ {x}^(3) } } ​

Question

If x is positive, is


`\sqrt{ \frac{1}{ { {x} }^(2) } }`
greater than, less than, or equal to

`\sqrt[3]{ \frac{1}{ {x}^(3) } }`
​

Answer 1

They are equal.

`\sqrt{\frac1{x^2}} = \frac1 = \frac1x`

since
`x>0`, and

`\sqrt[3]{\frac1{x^3}} = \frac1x`