Expert: Ahmed Salami - 1/29/2006

Question
I understand that if you are taking the cube root of 3 and multiplying it to the cube root of 9, you would multiply the two bases and take the cube root of that. But what if the bases are the same and the roots are different? Or what if you are multiplying the 4th root of 5 by the 4th root of 5? Thank you for your time.

Answer
Hi Lany,
Sorry for the time it took. Technical problem with the site.
These are problems requiring the use of the laws of
indices
(x^a).(x^b) = x^(a+b)
(x^a)/(x^b) = x^(a-b)
(x^a).(y^a) = (xy)^a
the nth root of x is written as x^(1/n)
also, (x^a)^b = x^(ab)
which are the basic ones.
So if we're multiplying, say, the fourth root of 5 by
the sixth root of 5, we have
5^(1/4) . 5^(1/6)
which by using our first rule becomes
5^(1/4 + 1/6) = 5^(5/12)

I hope i have helped. You can always get back to me.
Regards.