Question

Please answer my question quickly!

Answer 1

`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`