The simplified expression of [tex]\sqrt{\frac{162x^9}{2x^{27}}}[/tex] is [tex]\frac{9}{x^9}[/tex]
How to simplify the expression?
The expression is given as:
[tex]\sqrt{\frac{162x^9}{2x^{27}}}[/tex]
Divide 162 and 2 by 2
[tex]\sqrt{\frac{81x^9}{x^{27}}}[/tex]
Take the square root of 81
[tex]9\sqrt{\frac{x^9}{x^{27}}}[/tex]
Apply the quotient rule of indices
[tex]9\sqrt{\frac{1}{x^{27-9}}}[/tex]
Evaluate the difference
[tex]9\sqrt{\frac{1}{x^{18}}}[/tex]
Take the square root of x^18
[tex]\frac{9}{x^9}[/tex]
Hence, the simplified expression of [tex]\sqrt{\frac{162x^9}{2x^{27}}}[/tex] is [tex]\frac{9}{x^9}[/tex]
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