Question

How do you simplify `(25x^3)^(2/3) div (125xy^2) ^(1/3)`?

Answer 1

`x^2root3((5)/(xy^2)`

Explanation:

Recall: laws of indices:
`x^(1/3) = root3 x`
`x^m xx y^m = (xy)^m`

`(25x^3)^(2/1 xx1/3) div (125xy^2) ^(1/3)`

= `((25x^3)^(2/1 xxcolor(red)(1/3)))/ ((125xy^2) ^color(red)(1/3)) = " "[((25x^3)^(2/1))/(125xy^2)] ^color(red)(1/3)`

`[(25xx25x^6)/(125xy^2)] ^color(red)(1/3) = " " [(cancel25xxcancel25^5x^6)/(cancel125^cancel5xy^2)] ^color(red)(1/3)`

=`root3((5x^6)/(xy^2)`

=`x^2root3((5)/(xy^2)`