Question

Simplify 3(2x^4*y^5)^2/(6x^3*y^3)^6

Answer 1

$\dfrac{3(2x^4y^5)^2}{(6x^3y^3)^6}\qquad\text{use}\ (ab)^n=a^nb^n\ \text{and}\ (a^n)^m=a^{nm}\\\\=\dfrac{3(2^2)(x^4)^2(y^5)^2}{6^6(x^3)^6(y^3)^6}=\dfrac{3(4)x^8y^{10}}{46656x^{18}y^{18}}\qquad\text{use}\ a^n\cdot a^m=a^{n+m}\\\\=\dfrac{12x^8y^{10}}{46656x^8x^{10}y^{10}y^8}=\dfrac{1}{3888x^{10}y^8}$