Question

Simplify the square root of x to the power of 16 times y to the power of 36.

Answer 1

Answer:

$\large\boxed{x^8y^{18}}$

Step-by-step explanation:

$\sqrt{x^{16}\times y^{36}}\\\\\text{Use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\=\sqrt{x^{16}}\times \sqrt{y^{36}}\\\\\text{Use}\ (a^n)^m=a^{nm}\\\\=\sqrt{x^{8\cdot2}}\times\sqrt{y^{18\cdot2}}=\sqrt{(x^8)^2}\times\sqrt{(y^{18})^2}\\\\\text{Use}\ \sqrt{a^2}=|a|\\\\=|x^8|\times|y^{18}|\\\\\text{Because}\ x^8\geq0\ \text{and}\ y^{18}\geq0\ \text{for any value of x and y we have}\\\\=x^8\times y^{18}=x^8y^{18}$