Question

Please help!

Answer 1

\[\frac{ 216x ^{12} }{ 8x^3y^9 }\]

Answer 2

This one is much like the last one I helped you with, with another property tacked on. You can simplify the stuff inside the parentheses as a first step. Then, two more properties can be applied:

\[(a^n)^m = a^{n*m}\]and\[(\frac{a}{b})^m = \frac{a^m}{a^n}\]

Answer 3

\[\frac{ 27x ^{12-3} }{ y^9 }\]

Answer 4

\[\frac{ 27x ^{9} }{ y^9}\]

Answer 5

Thank you @Nurali

Answer 6

My Pleasure.

Answer 7

Now if you do it the way I suggested, you have:

\[(\frac{6x^4}{2xy^3})^3 = ({3x^3y^-3})^3 = 3^3x^{3*3}y^{-3*3} = 27x^9y^{-9} = \frac{27x^9}{y^9}\]saving you the trouble of reducing the larger fractions.

Answer 8

Let's make that neater:
\[(\frac{6x^4}{2xy^3})^3 = ({3x^3y^{-3}})^3 = 3^3x^{3*3}y^{-3*3} = 27x^9y^{-9} = \frac{27x^9}{y^9}\]