Question

Which expression is equivalent to √128x^5y^6/2x^7y^5? Assume x>0 and y>0.

Answer 1

`\sqrt{(128x^5y^6)/(2x^7y^5)}=\sqrt{(128)/(2)\cdot(x^5)/(x^7)\cdot(y^6)/(y^5)}=\sqrt{64\cdot(1)/(x^2)\cdot y}=√(64)\cdot\sqrt{(1)/(x^2)}\cdot√(y)=\\\\\\=8\cdot(1)/(x)\cdot√(y)=\boxed{(8√(y))/(x)}`

Answer D.

Answer 2

The correct option is D.

Explanation:

The given expression is,

`\sqrt{(128x^5y^6)/(2x^7y^5)}`

`\sqrt{(64x^5y^6)/(x^7y^5)}`

Use exponent rule
`(a^m)/(a^n)=a^(m-n)`,

`\sqrt{64x^(5-7)y^(6-5)}`

`\sqrt{64x^(-2)y^(6-5)}`

Use exponent rule
`a^(-n)=(1)/(a^n)`,

`\sqrt{64* (1)/(x^2)* y}`

`\sqrt{((8)/(x))^2* y}`

`(8√(y))/(x)`

Therefore option D is correct.