Multiplying different bases with different exponent

I'm doing a very basic pre algebra "refreshment", and for an assignment I need to simplify the following, leaving my answer as a single base raised to a single exponent:

9^2 * 12^3 * 2

I can't seem to find the steps needed to get the answer which is supposed to be 6^7. Normally I would look for common bases (like 9 and 27 have 3 in common), but I don't see that in 9 and 12.

Can someone explain this to me?

Re: Multiplying different bases with different exponent

Quote:

Originally Posted by

**timmeh** I'm doing a very basic pre algebra "refreshment", and for an assignment I need to simplify the following, leaving my answer as a single base raised to a single exponent:

9^2 * 12^3 * 2

I can't seem to find the steps needed to get the answer which is supposed to be 6^7. Normally I would look for common bases (like 9 and 27 have 3 in common), but I don't see that in 9 and 12.

Can someone explain this to me?

Hint: $\displaystyle 9=3^2$ and $\displaystyle 12=3\cdot 2^2$

Re: Multiplying different bases with different exponent

Ah now i see. Thanks.

(3^2)^2 * (3*2^2)^3

=> 3^4 * 3^3 * 2^6 * 2

=> 3^7 * 2^7

=> 6^7

That must be it, right? :)

Re: Multiplying different bases with different exponent

Quote:

Originally Posted by

**timmeh** Ah now i see. Thanks.

(3^2)^2 * (3*2^2)^3

=> 3^4 * 3^3 * 2^6 * 2

=> 3^7 * 2^7

=> 6^7

That must be it, right? :)

Yup! (Bigsmile)