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Please answer my question quickly!

Please answer my question quickly!-example-1

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Answer:


12^6, ? = 6

Explanation:

We are given instructions by the problem. When dividing exponential expressions with the same base, we can find the difference (subtraction) between the exponents and keep the base.


\displaystyle 12^9 / 12^3=12^(9-3)=12^6

But why does this work?

Let us write it out.


\displaystyle 12^9 / 12^3 = (12^9)/(12^3) =(12*12*12*12*12*12*12*12*12)/(12*12*12)

Now, 12 divided by 12 (aka
(12)/(12)) is equal to 1.


\displaystyle 1*1*1*12*12*12*12*12*12}

And anything times one is itself. Then, we can rewrite this as 12 to the power of 6 because we are multiplying 12 by itself 6 times.


\displaystyle 12*12*12*12*12*12} =12^6

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