The equivalent expression of [tex]\sqrt{\frac{55x^7y^6}{11x^{11}y^8}}[/tex] is [tex]\frac{1}{x^2y} \sqrt 5[/tex]
How to determine the equivalent expression?
The expression is given as:
[tex]\sqrt{\frac{55x^7y^6}{11x^{11}y^8}}[/tex]
Divide 55 by 11
[tex]\sqrt{\frac{5x^7y^6}{x^{11}y^8}}[/tex]
Apply the law of indices
[tex]\sqrt{\frac{5}{x^{11 -7}y^{8 - 6}}}[/tex]
Evaluate the differences
[tex]\sqrt{\frac{5}{x^{4}y^2}}[/tex]
Take the square root of x^4 and y^2
[tex]\frac{1}{x^2y} \sqrt 5[/tex]
Hence, the equivalent expression of [tex]\sqrt{\frac{55x^7y^6}{11x^{11}y^8}}[/tex] is [tex]\frac{1}{x^2y} \sqrt 5[/tex]
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