How do you simplify $\frac{6 x^{- \frac{4}{3}} \cdot 2 x^{\frac{2}{3}}}{2 x^{- \frac{1}{3}}}$ $[6x^(-4/3) * 2x^(2/3)] /( 2x^(-1/3))$ leaving only positive exponents?

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Answer 1 · 2016-07-18T22:30:33

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

$\frac{6 x^{- \frac{4}{3}} \cdot 2 x^{\frac{2}{3}}}{2 x^{- \frac{1}{3}}}$ $[6x^(-4/3) * 2x^(2/3)] /( 2x^(-1/3))$

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

= $[6 xx color(blue)(x^(-4/3)) xx cancel2xx x^(2/3)] /( cancel2 xx color(red)(x^(-1/3))) " "x^-m = 1/x^m$

$[6 xx color(red)(x^(1/3)) xx x^(2/3)] /(color(blue)( x^(4/3)))$

= $[6 xx x^(3/3)] /( x^(4/3)) " "1/3+2/3 = 3/3$

= $6/x^(1/3)" "4/3 - 3/3 = 1/3$

How do you simplify [6x^(-4/3) * 2x^(2/3)] /( 2x^(-1/3))6x−43⋅2x232x−13[6x^(-4/3) * 2x^(2/3)] /( 2x^(-1/3)) leaving only positive exponents?