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umka21 [38]3 years ago

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The simplified expression of $\sqrt{\frac{162x^9}{2x^{27}}}$ is $\frac{9}{x^9}$

<h3>How to simplify the expression?</h3>

The expression is given as:

$\sqrt{\frac{162x^9}{2x^{27}}}$

Divide 162 and 2 by 2

$\sqrt{\frac{81x^9}{x^{27}}}$

Take the square root of 81

$9\sqrt{\frac{x^9}{x^{27}}}$

Apply the quotient rule of indices

$9\sqrt{\frac{1}{x^{27-9}}}$

Evaluate the difference

$9\sqrt{\frac{1}{x^{18}}}$

Take the square root of x^18

$\frac{9}{x^9}$

Hence, the simplified expression of $\sqrt{\frac{162x^9}{2x^{27}}}$ is $\frac{9}{x^9}$