Which expression is equivalent to 3^2 • 3^–5? A. 1/3^3 B. 1/3^7 C. 1/3^-3 D. 1/3^-7

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Which expression is equivalent to 3^2 • 3^–5? A. 1/3^3 B. 1/3^7 C. 1/3^-3 D. 1/3^-7

Mathematics
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Use the rule \[\LARGE x^{\color{red}{a}}*x^{\color{blue}{b}} = x^{\color{red}{a}+\color{blue}{b}}\]
For example \[\LARGE x^{\color{red}{2}}*x^{\color{blue}{3}} = x^{\color{red}{2}+\color{blue}{3}}=x^{5}\]
so is it C?

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Other answers:

what do you get when you use that rule (ignore the answer choices right now)
-3
write out the whole thing, not just the exponent
|dw:1442278377207:dw|
I meant to include the base
why?
look back at the rule I posted
yes it's addition
i know
so what does \(\LARGE 3^2*3^{-5}\) turn into when you use that rule?
3^-3
good
next comes the rule \[\LARGE x^{-a} = \frac{1}{x^a}\]
ohh so it's 1/3^-3
close
do you see in the last rule how the `-a` exponent turned into `a` (without the negative) ?
yes
so basically that rule is saying "if the exponent is negative, you take the reciprocal of the base to make the exponent positive"
example \[\LARGE 2^{-7} = \frac{1}{2^7}\]
ok so that means it is not negative anymore so that the answer will be 1/3^3 right?
yes, \[\LARGE 3^{-3} = \frac{1}{3^3}\]
thank you very much!!!
no problem

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