How do you simplify [6x^(-4/3) * 2x^(2/3)] /( 2x^(-1/3)) leaving only positive exponents?

Jul 18, 2016

$\frac{6}{x} ^ \left(\frac{1}{3}\right)$

Explanation:

$\frac{6 {x}^{- \frac{4}{3}} \cdot 2 {x}^{\frac{2}{3}}}{2 {x}^{- \frac{1}{3}}}$

For ease of working, separate the coefficients from the variables - only the variables have indices to be attended to!

=$\frac{6 \times \textcolor{b l u e}{{x}^{- \frac{4}{3}}} \times \cancel{2} \times {x}^{\frac{2}{3}}}{\cancel{2} \times \textcolor{red}{{x}^{- \frac{1}{3}}}} \text{ } {x}^{-} m = \frac{1}{x} ^ m$

$\frac{6 \times \textcolor{red}{{x}^{\frac{1}{3}}} \times {x}^{\frac{2}{3}}}{\textcolor{b l u e}{{x}^{\frac{4}{3}}}}$

=$\frac{6 \times {x}^{\frac{3}{3}}}{{x}^{\frac{4}{3}}} \text{ } \frac{1}{3} + \frac{2}{3} = \frac{3}{3}$

=$\frac{6}{x} ^ \left(\frac{1}{3}\right) \text{ } \frac{4}{3} - \frac{3}{3} = \frac{1}{3}$