Question

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

Answer 1

`6/x^(1/3)`

Explanation:

`[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`