So what you wanted to do here is use the rule of `a power in a power`, which is this:
\(\sf\color{gray}{\text{If a base is raised to a power that is then raised to another power} \\ \text{you multiply the two powers together}}\)
Using this rule, you use the -2 power associated on the outside of the parenthesis and multiply every power inside of it by -2.
Ferrari:
okay i don't really understand that i have to do this quickly
Ferrari:
i'll just do it tomorrow :|
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Ferrari:
????????
Juss1Jordan:
With what?
jhonyy9:
use this
\[x^{-2} = \frac{ 1 }{ x^{2} }\]
Extrinix:
Here, I'll draw up the equations
\(\color{gray}{\sf{\huge{(}}\dfrac{y^{-2}z^3}{z^{-4}y^5}{\huge{)^{-2}}}}\)
That's what it normally looks like, but this is what the -2 does
\(\color{gray}{\sf{\huge{(}}\dfrac{y^{4}z^{-6}}{z^{8}y^{-10}}{\huge{)}}}\)
Now from that, you can divide both of them, using the rule of power division, which is below
\(\sf{\color{gray}{\text{If an exponent with the same base variable is divided by a similar variable, } \\ \text{the exponent of the numerator is subtracted by the exponent of the denominator.}}}\)
This would give you
\(\sf\color{gray}{y^{(4)-(-10)} z^{(-6)-(8)}}\)
Extrinix:
Whoops sorry jhonyy, didn't see you typing
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jhonyy9:
@extrinix wrote:
So what you wanted to do here is use the rule of `a power in a power`, which is this:
\(\sf\color{gray}{\text{If a base is raised to a power that is then raised to another power} \\ \text{you multiply the two powers together}}\)
Using this rule, you use the -2 power associated on the outside of the parenthesis and multiply every power inside of it by -2.
please explain it why ?
so bc.
\[\left( \left( x^{b} \right)^{a} \right) = x^{a*b}\]
jhonyy9:
@extrinix wrote:
Here, I'll draw up the equations
\(\color{gray}{\sf{\huge{(}}\dfrac{y^{-2}z^3}{z^{-4}y^5}{\huge{)^{-2}}}}\)
That's what it normally looks like, but this is what the -2 does
\(\color{gray}{\sf{\huge{(}}\dfrac{y^{4}z^{-6}}{z^{8}y^{-10}}{\huge{)}}}\)
Now from that, you can divide both of them, using the rule of power division, which is below
\(\sf{\color{gray}{\text{If an exponent with the same base variable is divided by a similar variable, } \\ \text{the exponent of the numerator is subtracted by the exponent of the denominator.}}}\)
This would give you
\(\sf\color{gray}{y^{(4)-(-10)} z^{(-6)-(8)}}\)