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 t…

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)`