Question

How do you convert powers to the same base if the bases don't have common factors?

Example:


`3^(2) * 2^(2)`
Yes, I know how to solve that, but how would you convert them to the same bases?

Answer 1

6²

Explanation:

Use the rule of exponents ...

(a·b)^c = a^c·b^c

Your expression has a=3, b=2, c=2.

3²·2² = (3·2)² = 6²

_____

If you want to get more sophisticated than that, logarithms can get involved.

`3^2\cdot 2^2=10^{2\log{(3)}+2\log{(2)}}\approx 10^(1.5563025)`