Question

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

Answer 1

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