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

Mohit Athwani asked Nov 16, 2023

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3 votes

If x is positive, is

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

$\sqrt[3]{ \frac{1}{ {x}^(3) } }$

Mohit Athwani asked Nov 16, 2023

2.8k points

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8 votes

They are equal.

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

since
x>0 , and

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

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