SOLUTION: Simplify the 5th square root of x^3y^2 10th square root of x^4y^16

Question 656225: Simplify the 5th square root of x^3y^2 10th square root of x^4y^16
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
First of all, there are no such things as "5th square root" or "10th square root". I'm guessing what you mean is:

If this is correct then I think working with these expressions will be easier for you if you learn what they are. The first radical represents a "5th root" not a "5th square root" and the second one is a "10th root" not a "10th square root". The absence of the word "square" is important. The first one represents whatever expression you could raise to the 5th power and get as a result. And the second one represents whatever expression you could raise to the 10th power and get as a result.

I think the easiest way to simplify this expression is to use fractional exponents. For 5th roots the exponent is 1/5 and for 10th roots the exponent is 1/10. So we can rewrite the expression using these exponents instead of the radicals:

Now we can start using our rules for exponents to simplify. First we will raise to 1/5 and 1/10 powers using the rule:

Now we can use the power of a power rule, :

which simplifies as follows:

And finally we can use the rule to multiply the x's and y's:

which simplifies as follows:

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