Question

simplify the expression (4x^2y^3)^3

Answer 1

\[(4x^2y^3)^3=(4x^2y^3)*(4x^2y^3)*(4x^2y^3)\]Taking the first two,\[(4x^2y^3)*(4x^2y^3)=16x^44x^2y^3*4x^2y^3y^6\]Factorizing,\[(4x^2y^3)*(4x^2y^3)=4x^2y^3(16x^4y^6)\]Therefore,\[(4x^2y^3)*(4x^2y^3)*(4x^2y^3)=(4x^2y^3)*(4x^2y^3)(16x^4y^6)\]This way,\[(4x^2y^3)^3=(4x^2y^3)(16x^4y^6)(16x^4y^6)\]Which is the same as,\[(4x^2y^3)^3=(4x^2y^3)(16x^4y^6)^2\]Which you should know, is a notable product.

Answer 2

\[(xy)^3=xy(x^2y^2)^2\]