Question

Simplify

√63x^15y^9/√7xy^11

Please don’t guess I need to get this right!! :)

Answer 1

`\large\boxed{\frac{\sqrt{63x^(15)y^9}}{\sqrt{7xy^(11)}}=(3\cdot x^7)/(y)=(3x^7)/(y)}`

Explanation:

`\frac{\sqrt{63x^(15)y^9}}{\sqrt{7xy^(11)}}\\\\\text{use}\ \sqrt{(a)/(b)}=(√(a))/(√(b))\\\\=\sqrt{(63\!\!\!\!\!\diagup^9x^(15)y^9)/(7\!\!\!\!\diagup_1xy^(11))}=\sqrt{(9x^(15)y^9)/(xy^(11))}\\\\\text{Cancel x and y respectively}\\\\=\sqrt{(9x^(14))/(y^2)}\\\\\text{use}\ \sqrt{(a)/(b)}=(√(a))/(√(b))\ \text{and}\ √(ab)=√(a)\cdot√(b)\\\\=\frac{\sqrt9\cdot\sqrt{x^(11)}}{√(y^2)}\\\\\text{use}\ (a^n)^m=a^(nm)`

`=\frac{√(3^2)\cdot\sqrt{x^(7\cdot2)}}{√(y^2)}=(√(3^2)\cdot√((x^7)^2))/(√(y^2))\\\\\text{use}\ √(a^2)=a\\\\=(3\cdot x^7)/(y)=(3x^7)/(y)`