tootsi123
  • tootsi123
How would i work this problem.... zy^6/z^7y^5 @Hero
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
you apply laws for exponents
tootsi123
  • tootsi123
what exactly are those laws??
jim_thompson5910
  • jim_thompson5910
|dw:1440102893950:dw|

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jim_thompson5910
  • jim_thompson5910
the z up top is really \(\Large z^1\) |dw:1440102934841:dw|
jim_thompson5910
  • jim_thompson5910
|dw:1440102979430:dw|
jim_thompson5910
  • 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
jim_thompson5910
  • 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
tootsi123
  • tootsi123
|dw:1440102880698:dw| is that right
jim_thompson5910
  • jim_thompson5910
very good, so you have \[\Large z^{-6}y\]
tootsi123
  • tootsi123
Okay that makes a little more sense. :)
jim_thompson5910
  • 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
tootsi123
  • tootsi123
So if you want it to be positive you put the negative on the bottom?
imqwerty
  • 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-\[\frac{ zy^6 }{ z^7 y^5}--->z^{1-7} y ^{6-5}\] \[z ^{-6} y\]
tootsi123
  • tootsi123
Thank you guys!!!
jim_thompson5910
  • 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?
tootsi123
  • tootsi123
yeah thats what i mean
imqwerty
  • 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?

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