AnonymousMathStudent AnonymousMathStudent
  • 18-11-2019
  • Mathematics
contestada

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

[tex]3^{2} * 2^{2}[/tex]
Yes, I know how to solve that, but how would you convert them to the same bases?

Respuesta :

sqdancefan
sqdancefan sqdancefan
  • 18-11-2019

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

_____

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

  [tex]3^2\cdot 2^2=10^{2\log{(3)}+2\log{(2)}}\approx 10^{1.5563025}[/tex]

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