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

1 Answer
Jul 18, 2016

Answer:

#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#