How do you simplify $root3(125x^21y^24)$ ?

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Answer 1 · 2016-05-11T06:31:27

$root(3)(125x^21y^24) = 5x^7y^8$

Notice that $(5x^7y^8)^3 = 5^3(x^7)^3(y^8)^3 = 125x^21y^24$

So $5x^7y^8$ is a cube root of $125x^21y^24$

Any Real number has a unique Real cube root, so for Real values of $x$ and $y$ and Real cube roots, we can deduce that this is the cube root we want.

How do you simplify root3(125x^21y^24)root3(125x^21y^24)?