Question

1. simplify (4x^4y^3)^3/3(5x^2y^6)^2
15 POINTS

Answer 1

`((4x^4y^3)^3)/(3(5x^2y^6)^2)\qquad\text{use}\ (ab)^n=a^nb^n\ \text{and}\ (a^n)^m=a^(nm)\\\\=(4^3(x^4)^3(y^3)^3)/(3(5^2)(x^2)^2(y^6)^2)=(64x^(12)y^9)/(3(25)x^4y^(12))=(64x^(12)y^9)/(75x^4y^(12))\qquad\text{use}\ (a^n)/(a^m)=a^(n-m)\\\\=(64)/(75)x^(12-4)y^(9-12)=(64)/(75)x^8y^(-3)=\boxed{(64x^8)/(75y^3)}`