250X^9y^5 all inside a 3rd root thing...
The answer is 5X^3 Y^3 and then a "2y^2" which is inside a square root thing.
Thanks a lot!
$\displaystyle \sqrt[3]{250 x^9 y^5}$
Since that is a cube root, set everything into cubes as much as possible.
250= 125* 2 and 125= 5*5*5= $\displaystyle 5^3$
$\displaystyle x^9= (x*x*x)(x*x*x)(x*x*x)= (x^3)^3$
$\displaystyle y^5= y*y*y*y*y= (y*y)(y*y*y)= y^2 y^3$
So what that is is $\displaystyle \sqrt[3]{2(5^3)(x^3)^3y^2y^3}$
Of course, the definition of "cube root" is that $\displaystyle \sqrt[3]{a^3}= a$.
$\displaystyle \sqrt[3]{250 x^9 y^5}= \sqrt[3]{2}\sqrt[3]{5^3}\sqrt[3]{(x^3)^3}\sqrt[3]{y^2}\sqrt[3]{y^3}$
$\displaystyle = \sqrt[3]{2}(5)(x^3)\sqrt[3]{y^2}y= 5x^3y\sqrt[3]{2y^2}$