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

Answer:

  6²

Step-by-step 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

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

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