Simplify ( 4x )^-1 ( 3x^3x )^2 ( 12x )^-3.

( 4x )^-1 ( 3x^3x )^2 ( 12x )^-3 = x4 (3x^2)^2 (2x)^3 = x4 9x^4 8x^3 = 18x^8.

jmc

algebra intermediate

Problem

Simplify

(\frac{4}{x})^{- 1} (\frac{3 x ^{3}}{x})^{2} (\frac{1}{2 x})^{- 3}

Solution

(\frac{4}{x})^{- 1} (\frac{3 x ^{3}}{x})^{2} (\frac{1}{2 x})^{- 3} = \frac{x}{4} \cdot (3 x^{2})^{2} \cdot (2 x)^{3} = \frac{x}{4} \cdot 9 x^{4} \cdot 8 x^{3} = 18 x^{8}

Final answer

18x^8