The equivalent expression of [tex]\sqrt{\frac{128x^5y^6}{2x^7y^5}}[/tex] is [tex]\frac{8\sqrt y}{x}[/tex]
How to determine the equivalent expression?
The expression is given as:
[tex]\sqrt{\frac{128x^5y^6}{2x^7y^5}}[/tex]
Divide 128 by 2
[tex]\sqrt{\frac{64x^5y^6}{x^7y^5}}[/tex]
Apply the law of indices to the variables
[tex]\sqrt{\frac{64y^{6-5}}{x^{7-5}}}[/tex]
Evaluate the differences
[tex]\sqrt{\frac{64y}{x^2}}[/tex]
Take the square root of 64
[tex]8\sqrt{\frac{y}{x^2}}[/tex]
Take the square root of x^2
[tex]\frac{8\sqrt y}{x}[/tex]
Hence, the equivalent expression of [tex]\sqrt{\frac{128x^5y^6}{2x^7y^5}}[/tex] is [tex]\frac{8\sqrt y}{x}[/tex]
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