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

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Answer 1 · 2016-09-06T18:11:36

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

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

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

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

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

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

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

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