## calculusxy one year ago Question with exponents! Question attached below...

1. calculusxy

$\huge \frac{ (-xy^4)^{-4} }{ -2x^3 \times x^2y^3 }$

2. anonymous

$(-2x^3)(x^2y^2) \implies -2 \cdot x^{3+2} \cdot y^2 =~?$

3. calculusxy

i got the answer of $\frac{ 1 }{ 2x^9y^19 }$ but the answer key says that it's negative.. i don't know why

4. anonymous

Alright let's check each step.

5. anonymous

what would you get for : $$\color{#0cbb34}{\text{Originally Posted by}}$$ @Jhannybean $\large (-2x^3)(x^2y^2) \implies -2 \cdot x^{3+2} \cdot y^2 =~?$ $$\color{#0cbb34}{\text{End of Quote}}$$

6. calculusxy

$\large -2x^5y^2$

7. anonymous

Alright, and when you distribute the $$-4$$ power into every term in the ( ), you expand it like so: $\large (-xy^4)^{-4} \implies (-x)^{-4} \cdot (y^4)^{-4} = ~?$

8. calculusxy

$\large -x^{-4} \times y^0$

9. calculusxy

which is basically like $\large -x^{-4}$

10. calculusxy

$\large \times$ do you mean this symbol? if so, it's multiplication.

11. anonymous

be careful, you wouldnt be adding the exponents here, you'd be multiplying them. $\large (y^4)^{-4} = y^{4( -4)}\qquad (y^4)^{-4} \ne y^{4-4}$

12. calculusxy

oh yes

13. calculusxy

i still don't understand how you got the negative...

14. calculusxy

yeah or whose ever work that was posted in the 3 parts

15. just_one_last_goodbye

pretty fast eh? ^_^ thinking about making it a tool on OS as an extention

16. anonymous

defeats the purpose of Openstudy then.

17. calculusxy

18. anonymous

Ok cotinuing from where we left off.

19. anonymous

I just realized theres an easier way to simplify the numerator, check this out

20. anonymous

Instead of expanding our numerator first, we can basically turn our entire term WITH the negative exponent into a positive one. $\large (-xy^4)^{-4} \implies \dfrac{1}{(-xy^4)^4}$ you see how the negatives in the numerator would go away?

21. anonymous

So now we expand our numerator, and we get: $\large \frac{1}{x^4y^{16}}$

22. anonymous

Now we put it over our denominator: $\large \dfrac{\dfrac{1}{x^4y^{16}}}{-2x^5y^3}\qquad \implies \qquad \dfrac{1}{-2x^{4+5}y^{16+3} }$

23. anonymous

Now whether we have the negative in the numerator OR denominator, it doesnt matter, the fraction altogether is STILL negative.

24. anonymous

Do you follow, @calculusxy ?

25. calculusxy

i am still trying to grasp this.

26. calculusxy

if we have like complex fractions, then we would have to add the exponents n put it over one?

27. anonymous

The only reason we did that, was because we treated $$(-xy^4)$$ as like a variable... let' say all that junk $$=a$$. And then... a is raised to a negative power, and how would we turn that power positive? by putting it over 1. $$a^{-1} \iff \dfrac{1}{a}$$

28. anonymous

So if we have a FRACTION in the numerator, and we're DIVIDING it by a term or terms in the denominator, we follow this rule: $\dfrac{\dfrac{a}{b}}{c} \implies \frac{a}{bc}$

29. calculusxy

okay...

30. calculusxy

i have one other question..

31. calculusxy

thanks for helping me understand that

32. anonymous

Which art are you stuck on? WE'll go from there.

33. anonymous

part*

34. calculusxy

so this time i am getting a negative, but it says that it's a positive. $\large -\frac{ ba^0 \times -a^3b^3 }{ (ab^0)^{-4} }$

35. calculusxy

so i got $\large -a^7b^4$ but the answer key simply says $\large a^7b^4$

36. calculusxy

@Jhannybean

37. calculusxy

@jim_thompson5910

38. calculusxy

@jim_thompson5910 it's the second expression w/ exponents.

39. jim_thompson5910

40. calculusxy

oh okay thx !