Question

Which expression is equivalent to square root 25x^9y^3/64x^6y^11

Answer 1

D is the correct answer on edge2021!!!

Answer 2

`\large\boxed{(5x√(x))/(8y^4)}`

Explanation:

`\sqrt{(25x^9y^3)/(64x^6y^(11))}\qquad\text{use}\ √(ab)=√(a)\cdot√(b),\ \sqrt{(a)/(b)}=(√(a))/(√(b));\ (a^m)/(a^n)=a^(m-n)\\\\=(√(25))/(√(64))\cdot \sqrt{x^(9-6)y^(3-11)}=(5)/(8)\sqrt{x^3y^(-8)}=(5)/(8)√(x^3)\cdot\sqrt{y^(-8)}\\\\\text{use}\ a^na^m=a^(n+m),\ (a^n)^m=a^(nm)\\\\=(5)/(8)\sqrt{x^(2+1)}\cdot\sqrt{y^((-4)(2))}=(5)/(8)√(x^2x)\cdot\sqrt{(y^(-4))^2}`

`=(5)/(8)√(x^2)\cdot√(x)\cdot\sqrt{(y^(-4))^2}\qquad\text{use}\ √(a^2)=a\ \text{for}\ a\geq0\\\\=(5)/(8)x√(x)\cdot y^(-4)\qquad\text{use}\ a^(-n)=(1)/(a^n)\\\\=(5x√(x))/(8y^4)`