What is the missing exponent?

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What is the missing exponent?

Mathematics
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Ok, we still work in the correct order of operations. In other words, let's work with the denominator first.\[\left(8^{-7}\right)^2 = 8^{-7}\times8^{-7}\]Here, you are multiplying, so what should that simplify to? (aka \(8^{??}\))
8^0???

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When you multiply, you add the exponents. You would get \(8^0\) if you subtracted them.
oh ok so its 8^-14
Yes. So, plugging that in again, \[\frac{8^{-5}}{8^{-14}} = 8^{?}\] We are dividing here.
dividing which ones
(im putting my baby bro. to sleep right now so i might type slow i only have 1 hand)
1 hand free*
(That's fine.) You're dividing in general, so you're going to have to either add or subtract the exponents. When you multiply, you added, so when you divide, you...?
subtract
so 8^9
9 is the answer?
Yes! Also, just in general, the only time you will multiply exponents (with the same bases, like here where you had 8 on the bottom) is when you have something like \(\left(8^3\right)^2\). This would simplify to \(8^6\) because what you're doing is \(8^3 \times8^3\).
ok tysm! You're so smart :D
So, for you to write down, you can say \(\left(a^b\right)^c = a^{bc}\)
i did
I GOT A 100!!!!!!!!!!
Good job!! :)
tysm!!! i gtg bye
np

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