## anonymous one year ago $\frac{(x ^{-5}x ^{4})^{4} }{ (x ^{4}x ^{-6})^{-5}}$

1. anonymous

How do i do this...Yes it may be simple but for some reason i can't figure it out.

2. TheSmartOne

Hint: First use this formula $$\sf(a^b)^c = a^{b\times c}$$ Then use this one $$\sf\Large\frac{a^b}{a^c}=a^{b-c}$$

3. anonymous

I know that

4. TheSmartOne

also these formulas: $$\sf a^b\times a^c = a^{b+c}$$ $$\sf\Large {a^{-b}}=\frac{1}{a^b}$$

5. anonymous

yes i understand that...i just can't seem to get the correct answer to this...

6. phi

can you simplify $x ^{-5}x ^{4}$? (add the exponents)

7. anonymous

x^-1

8. phi

yes now we have up top $(x^{-1})^4$ now use the rule multiply exponents to simplify that

9. anonymous

X^-4

10. phi

now let's do the bottom. first $(x ^{4}x ^{-6})$

11. anonymous

x^-2

12. phi

now (x^-2)^-5

13. anonymous

x^10

14. phi

so we have $\frac{x^{-4}}{x^{10} }$

15. anonymous

so 1/ x^14

16. phi

you can do that two ways: "flip" x^-4 and put it in the bottom but with x^4 then combine x^4*x^10 (in the bottom) or do -4 - 10 (subtract the exponents because we divide)

17. phi

yes 1/x^14 this can also be written x^(-14)

18. anonymous

ok thank you!