Spring98
  • Spring98
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
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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jim_thompson5910
  • jim_thompson5910
Use the rule \[\LARGE x^{\color{red}{a}}*x^{\color{blue}{b}} = x^{\color{red}{a}+\color{blue}{b}}\]
jim_thompson5910
  • jim_thompson5910
For example \[\LARGE x^{\color{red}{2}}*x^{\color{blue}{3}} = x^{\color{red}{2}+\color{blue}{3}}=x^{5}\]
Spring98
  • Spring98
so is it C?

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More answers

jim_thompson5910
  • jim_thompson5910
what do you get when you use that rule (ignore the answer choices right now)
Spring98
  • Spring98
-3
jim_thompson5910
  • jim_thompson5910
write out the whole thing, not just the exponent
Spring98
  • Spring98
|dw:1442278377207:dw|
jim_thompson5910
  • jim_thompson5910
I meant to include the base
Spring98
  • Spring98
why?
jim_thompson5910
  • jim_thompson5910
look back at the rule I posted
Spring98
  • Spring98
yes it's addition
Spring98
  • Spring98
i know
jim_thompson5910
  • jim_thompson5910
so what does \(\LARGE 3^2*3^{-5}\) turn into when you use that rule?
Spring98
  • Spring98
3^-3
jim_thompson5910
  • jim_thompson5910
good
jim_thompson5910
  • jim_thompson5910
next comes the rule \[\LARGE x^{-a} = \frac{1}{x^a}\]
Spring98
  • Spring98
ohh so it's 1/3^-3
Spring98
  • Spring98
@jim_thompson5910
jim_thompson5910
  • jim_thompson5910
close
jim_thompson5910
  • jim_thompson5910
do you see in the last rule how the `-a` exponent turned into `a` (without the negative) ?
Spring98
  • Spring98
yes
jim_thompson5910
  • jim_thompson5910
so basically that rule is saying "if the exponent is negative, you take the reciprocal of the base to make the exponent positive"
jim_thompson5910
  • jim_thompson5910
example \[\LARGE 2^{-7} = \frac{1}{2^7}\]
Spring98
  • Spring98
ok so that means it is not negative anymore so that the answer will be 1/3^3 right?
jim_thompson5910
  • jim_thompson5910
yes, \[\LARGE 3^{-3} = \frac{1}{3^3}\]
Spring98
  • Spring98
thank you very much!!!
jim_thompson5910
  • jim_thompson5910
no problem

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