## Spring98 one year ago 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

1. jim_thompson5910

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

2. jim_thompson5910

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

3. Spring98

so is it C?

4. jim_thompson5910

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

5. Spring98

-3

6. jim_thompson5910

write out the whole thing, not just the exponent

7. Spring98

|dw:1442278377207:dw|

8. jim_thompson5910

I meant to include the base

9. Spring98

why?

10. jim_thompson5910

look back at the rule I posted

11. Spring98

12. Spring98

i know

13. jim_thompson5910

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

14. Spring98

3^-3

15. jim_thompson5910

good

16. jim_thompson5910

next comes the rule $\LARGE x^{-a} = \frac{1}{x^a}$

17. Spring98

ohh so it's 1/3^-3

18. Spring98

@jim_thompson5910

19. jim_thompson5910

close

20. jim_thompson5910

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

21. Spring98

yes

22. 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"

23. jim_thompson5910

example $\LARGE 2^{-7} = \frac{1}{2^7}$

24. Spring98

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

25. jim_thompson5910

yes, $\LARGE 3^{-3} = \frac{1}{3^3}$

26. Spring98

thank you very much!!!

27. jim_thompson5910

no problem