SOLUTION: write in exponential form and simplify 3sqrta times 5sqrta the 3 and 5 are small just outside the root symbol. please help i have no idea how to do this.

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: write in exponential form and simplify 3sqrta times 5sqrta the 3 and 5 are small just outside the root symbol. please help i have no idea how to do this.      Log On


   

Question 285144: write in exponential form and simplify 3sqrta times 5sqrta the 3 and 5 are small just outside the root symbol. please help i have no idea how to do this.
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
If the expression is
root%283%2C+a%29%2Aroot%285%2C+a%29
then these are not square roots. The first one is a 3rd root (aka cube root). It represents whatever you cube to get "a". And the second one is a 5th root (what ever you raise to the 5th power to get "a").

To simplify this expression, you do what it says: "write in exponential form." Any radical can be rewritten using fractional exponents:
sqrt%28x%29+=+root%282%2C+x%29+=+x%5E%281%2F2%29
root%283%2C+x%29+=+x%5E%281%2F3%29
root%284%2C+x%29+=+x%5E%281%2F4%29
root%285%2C+x%29+=+x%5E%281%2F5%29
etc.

Rewriting your radcials with fractional exponents we get:
a%5E%281%2F3%29%2Aa%5E%281%2F5%29
And the rule for exponents when multiplying like this is to add the exponents. This gives us:
a%5E%281%2F3%2B1%2F5%29
To add the exponents, which are fractions, we need a common denominator:
a%5E%285%2F15%2B3%2F15%29
a%5E%288%2F15%29
This may be an acceptable answer. But if you want to rewrite this back in radical form:
%28a%5E8%29%5E%281%2F15%29
root%2815%2C+a%5E8%29