Question

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

Answer 1

Use the rule
\[\LARGE x^{\color{red}{a}}*x^{\color{blue}{b}} = x^{\color{red}{a}+\color{blue}{b}}\]

Answer 2

For example
\[\LARGE x^{\color{red}{2}}*x^{\color{blue}{3}} = x^{\color{red}{2}+\color{blue}{3}}=x^{5}\]

Answer 3

so is it C?

Answer 4

what do you get when you use that rule (ignore the answer choices right now)

Answer 5

-3

Answer 6

write out the whole thing, not just the exponent

Answer 7

I meant to include the base

Answer 8

why?

Answer 9

look back at the rule I posted

Answer 10

yes it's addition

Answer 11

i know

Answer 12

so what does \(\LARGE 3^2*3^{-5}\) turn into when you use that rule?

Answer 13

3^-3

Answer 14

good

Answer 15

next comes the rule

\[\LARGE x^{-a} = \frac{1}{x^a}\]

Answer 16

ohh so it's 1/3^-3

Answer 17

@jim_thompson5910

Answer 18

close

Answer 19

do you see in the last rule how the `-a` exponent turned into `a` (without the negative) ?

Answer 20

yes

Answer 21

so basically that rule is saying "if the exponent is negative, you take the reciprocal of the base to make the exponent positive"

Answer 22

example

\[\LARGE 2^{-7} = \frac{1}{2^7}\]

Answer 23

ok so that means it is not negative anymore so that the answer will be 1/3^3 right?

Answer 24

yes,

\[\LARGE 3^{-3} = \frac{1}{3^3}\]

Answer 25

thank you very much!!!

Answer 26

no problem