Question

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

Answer 1

`\large\boxed{x^8y^(18)}`

Explanation:

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