Question

Which expression is equivalent to Assume x 0 and y > 0.

Answer 1

Given radical expression:
`\sqrt{(25x^9y^3)/(64x^6y^(11))}`

`\mathrm{Apply\:exponent\:rule}:\quad (x^a)/(x^b)\:=\:x^(a-b)`

`(x^9)/(x^6)=x^(9-6)=x^3`

`(y^3)/(y^(11))=(1)/(y^(11-3))=(1)/(y^8)`

`\sqrt{(25x^9y^3)/(64x^6y^(11))} =\sqrt{(25x^3)/(64y^8)}`

`=(√(25)√(x^3))/(√(64)√(y^8))`

`√(25)=5`

`√(64)=8`

`=(5√(x^3))/(8√(y^8))`

`√(x^3)=x√(x)`

`√(y^8)=y^4`

Therefore,

`(5√(x^3))/(8√(y^8)) =(5x√(x))/(8y^4)`.

Therefore,
`\sqrt{(25x^9y^3)/(64x^6y^(11))}=(5x√(x))/(8y^4).`