SOLUTION: cube root (x^2y^4) x cube root (x^4y^10) i got : x^2 cube root(y^10) is this correct

Question 408332: cube root (x^2y^4) x cube root (x^4y^10)
i got : x^2 cube root(y^10) is this correct
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
Please don't use "x" for multiplication. Use the word "times" or use "*" (Shift+8).

Your answer, is correct so far but it is unfinished. There is more simplifying we can do with the remaining cube root.

is not a perfect cube. (Variables are perfect cubes if their exponents are multiples of 3.) But it does have perfect cube factors. Factoring the into as many perfect cube factors as possible we get:

Now we can use a property of radicals, to separate the factors inside the cube root into separate cube roots:

The cube roots of the perfect cubes will simplify:

which simplifies to:

This is the fully simplified expression.
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