## tootsi123 one year ago How would i work this problem.... zy^6/z^7y^5 @Hero

1. anonymous

you apply laws for exponents

2. tootsi123

what exactly are those laws??

3. jim_thompson5910

|dw:1440102893950:dw|

4. jim_thompson5910

the z up top is really $$\Large z^1$$ |dw:1440102934841:dw|

5. jim_thompson5910

|dw:1440102979430:dw|

6. jim_thompson5910

the exponent law sourwing is referring to is this $\LARGE \frac{x^a}{x^b} = x^{a-b}$ if the bases are both the same, then you subtract the exponents

7. jim_thompson5910

so for example, focus on just the y terms |dw:1440103051004:dw| the exponents are 6 and 5. Subtract to get 6-5 = 1 that means $\Large \frac{y^6}{y^5} = y^{6-5} = y^1 = y$ you'll do the same for the z terms as well

8. tootsi123

|dw:1440102880698:dw| is that right

9. jim_thompson5910

very good, so you have $\Large z^{-6}y$

10. tootsi123

Okay that makes a little more sense. :)

11. jim_thompson5910

optionally the negative exponent can be made positive using this rule $\Large x^{-k} = \frac{1}{x^k}$ so $\Large z^{-6}y = \frac{1}{z^6}y = \frac{y}{z^6}$ again, this is optional since some books I've seen want you to rewrite with positive exponents

12. tootsi123

So if you want it to be positive you put the negative on the bottom?

13. imqwerty

so we are given -$\frac{ zy^6 }{ z^7 y^5 }$ we know that $\frac{ a^x }{a^y } = a^(x-y)$ so we get-$\frac{ zy^6 }{ z^7 y^5}--->z^{1-7} y ^{6-5}$ $z ^{-6} y$

14. tootsi123

Thank you guys!!!

15. jim_thompson5910

So if you want it to be positive you put the negative on the bottom? I'm not sure what you mean, but I think you mean to just flip the fraction to make the exponent positive. Right?

16. tootsi123

yeah thats what i mean

17. imqwerty

welcome :) u mean that - if u got $z ^{2}$then to make the power negative u can write it as $\frac{ 1 }{z ^{-2}}$correct?