## anonymous 5 years ago how can you write a experession as a single exponent?

1. anonymous

Depends on the expression

2. anonymous

okay $3^{2} - 3^{3}$

3. anonymous

Ok, to do this you will need to factor a bit. Do you know how to factor?

4. anonymous

yes

5. anonymous

Ok, so we can rewrite this expression like this: $3^2 - 3^3 = 3^2 - (3^2*3)$ Right?

6. anonymous

yes

7. anonymous

Now factor out a $$3^2$$ from each term, and what do you get?

8. anonymous

$3^{5} \right$

9. anonymous

i mean $3^{5}$

10. anonymous

No. $3^2 - 3^2(3) = 3^2(\frac{3^2}{3^2} -\frac{3^2( 3)}{3^2}) = 3^2(1-3)$

11. anonymous

Recall how to factor something 5(3) + 5(100) = 5(3+100) = 5(103)

12. anonymous

17-17(23) = 17(1-23) = 17(-22)

13. anonymous

Or if you prefer you can think of it the other way. $3^2 - 3(2^2) = 1(3^2) - 3(3^2) = -2(3^2)$

14. anonymous

Ack.. that should be $3^2 - 3(3^2)$ before the first equals

15. anonymous

Did I lose you?

16. anonymous

yeah alot

17. anonymous

Ok lets try this a different way. Forget what I said before. Ok

18. anonymous

ok

19. anonymous

$3^2 - 3^3$ $= 1(3^2) - 3(3^2)$ With me so far?

20. anonymous

Do you see how these two things are equal?

21. anonymous

yes

22. anonymous

Ok, so now I tell you, you have 1x and you subtract 3x, what will you have?

23. anonymous

-3 right?

24. anonymous

-2x

25. anonymous

ok i get it

26. anonymous

So here, you have $$1(3^2)$$ and you subtract $$3(3^2)$$, what will you have?

27. anonymous

-18

28. anonymous

Well yes, but that's not an expression with 1 exponent.

29. anonymous

Although you could write it as $$-18^1$$ if you want to be a smart retrice;p

30. anonymous

I think they want you to write it as $$-2(3^2)$$

31. anonymous

ok

32. anonymous

I could be wrong though.

33. anonymous

how?

34. anonymous

it should be 3^-1

35. anonymous

Wait a minute, that is not correct

36. anonymous

im confused now

37. anonymous

It's -18 or $$-2(3^2)$$. It's the same number, it just depends on how your teacher wants to see it.