Exponents question (will be attached below) MEDAL will be award

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Exponents question (will be attached below) MEDAL will be award

Mathematics
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\[\frac{ y^{-1} \times -x^4y^3 }{ (x^0y^3)^3 }\]

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the answer key says that the answer is \[-\frac{ x^4 }{ y^7 }\] but i get the same answer but positive
-x^4 is negative so the final result will be negative.
but doesn't the eve n number exponent turn the negative base into a positive?
The negative In front of \(-x^4\) is not in front of an exponent -x^4 Is different from \(x^{-4}\)
so if it was in front of the exponent then it would have become \[\frac{ 1 }{ x^4 }\]?
If it was attached to the exponent then yes
So to summarize \[(-x)^{2}\neq-x^2\] and \[x^{-2}=\frac{ 1 }{ x^2 }\]
When dealing with negative NUMBERS and positive exponents the rule is this: The exponent only attaches to the NUMBER or the parentheses. It does not attach to the sign. If you want the sign to be included in the operation with the exponent then you must have the sign in the parentheses.... Like this...
\[-x^2=-(x)(x)=-x^2\]
\[(-x)^2=(-x)(-x)=x^2\]
\[-(x)^2=-(x)(x)=-x^2\]
So the exponent makes the thing it is attached to repeatedly multiply the number of times the exponent says. It will only attach to a number, or set pf parentheses. If it attaches to the number only repeatedly multiply the number and not the sign. If the exponent is attached to the parentheses then repeatedly multiply whatever is in the parentheses. Hope that helps
@calculusxy did you understand this question? :)

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