How do negative exponents affect the + and - signs in a fraction

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I understand that when such a fractions has an even exponent the sign becomes the opposite. Like such: $(-frac12)^4 = (+frac12)$. Right?



I don't know what sign this $(-frac12)^
-4$ will have by the end.




algebra-precalculus




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  • $$left(-frac 12right)^-4 = left(frac 1-frac 12right)^4= (-2)^4 = +16$$ Note that $left(-frac 12right)^4 = frac 116$ which is positive.
    – amWhy
    Aug 5 at 23:05















up vote
-1
down vote

favorite












I understand that when such a fractions has an even exponent the sign becomes the opposite. Like such: $(-frac12)^4 = (+frac12)$. Right?



I don't know what sign this $(-frac12)^
-4$ will have by the end.




algebra-precalculus




share|cite|improve this question



















  • $$left(-frac 12right)^-4 = left(frac 1-frac 12right)^4= (-2)^4 = +16$$ Note that $left(-frac 12right)^4 = frac 116$ which is positive.
    – amWhy
    Aug 5 at 23:05













up vote
-1
down vote

favorite









up vote
-1
down vote

favorite











I understand that when such a fractions has an even exponent the sign becomes the opposite. Like such: $(-frac12)^4 = (+frac12)$. Right?



I don't know what sign this $(-frac12)^
-4$ will have by the end.




algebra-precalculus




share|cite|improve this question











I understand that when such a fractions has an even exponent the sign becomes the opposite. Like such: $(-frac12)^4 = (+frac12)$. Right?



I don't know what sign this $(-frac12)^
-4$ will have by the end.





algebra-precalculus





share|cite|improve this question










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asked Aug 5 at 23:00









Daniel Montilla

1




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  • $$left(-frac 12right)^-4 = left(frac 1-frac 12right)^4= (-2)^4 = +16$$ Note that $left(-frac 12right)^4 = frac 116$ which is positive.
    – amWhy
    Aug 5 at 23:05

















  • $$left(-frac 12right)^-4 = left(frac 1-frac 12right)^4= (-2)^4 = +16$$ Note that $left(-frac 12right)^4 = frac 116$ which is positive.
    – amWhy
    Aug 5 at 23:05
















$$left(-frac 12right)^-4 = left(frac 1-frac 12right)^4= (-2)^4 = +16$$ Note that $left(-frac 12right)^4 = frac 116$ which is positive.
– amWhy
Aug 5 at 23:05





$$left(-frac 12right)^-4 = left(frac 1-frac 12right)^4= (-2)^4 = +16$$ Note that $left(-frac 12right)^4 = frac 116$ which is positive.
– amWhy
Aug 5 at 23:05











1 Answer
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When you are confused, return to the definitions. The definition of $(-1/4)^4$ is



$$left(-frac14right)left(-frac14right)left(-frac14right)left(-frac14right)=frac1256.$$



When we have a negative number for the exponent, we have



$$left(-frac14right)^-4=frac1left(-frac14right)^4=frac1frac1256=256.$$






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    The question is about $left(-frac 12right)^4$. and $left(-frac 12right)^-4$
    – amWhy
    Aug 5 at 23:07











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1 Answer
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1 Answer
1






active

oldest

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active

oldest

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up vote
1
down vote













When you are confused, return to the definitions. The definition of $(-1/4)^4$ is



$$left(-frac14right)left(-frac14right)left(-frac14right)left(-frac14right)=frac1256.$$



When we have a negative number for the exponent, we have



$$left(-frac14right)^-4=frac1left(-frac14right)^4=frac1frac1256=256.$$






share|cite|improve this answer



















  • 1




    The question is about $left(-frac 12right)^4$. and $left(-frac 12right)^-4$
    – amWhy
    Aug 5 at 23:07















up vote
1
down vote













When you are confused, return to the definitions. The definition of $(-1/4)^4$ is



$$left(-frac14right)left(-frac14right)left(-frac14right)left(-frac14right)=frac1256.$$



When we have a negative number for the exponent, we have



$$left(-frac14right)^-4=frac1left(-frac14right)^4=frac1frac1256=256.$$






share|cite|improve this answer



















  • 1




    The question is about $left(-frac 12right)^4$. and $left(-frac 12right)^-4$
    – amWhy
    Aug 5 at 23:07













up vote
1
down vote










up vote
1
down vote









When you are confused, return to the definitions. The definition of $(-1/4)^4$ is



$$left(-frac14right)left(-frac14right)left(-frac14right)left(-frac14right)=frac1256.$$



When we have a negative number for the exponent, we have



$$left(-frac14right)^-4=frac1left(-frac14right)^4=frac1frac1256=256.$$






share|cite|improve this answer















When you are confused, return to the definitions. The definition of $(-1/4)^4$ is



$$left(-frac14right)left(-frac14right)left(-frac14right)left(-frac14right)=frac1256.$$



When we have a negative number for the exponent, we have



$$left(-frac14right)^-4=frac1left(-frac14right)^4=frac1frac1256=256.$$







share|cite|improve this answer















share|cite|improve this answer



share|cite|improve this answer








edited Aug 5 at 23:15









amWhy

189k25219431




189k25219431











answered Aug 5 at 23:04









Elliot G

9,75121645




9,75121645







  • 1




    The question is about $left(-frac 12right)^4$. and $left(-frac 12right)^-4$
    – amWhy
    Aug 5 at 23:07













  • 1




    The question is about $left(-frac 12right)^4$. and $left(-frac 12right)^-4$
    – amWhy
    Aug 5 at 23:07








1




1




The question is about $left(-frac 12right)^4$. and $left(-frac 12right)^-4$
– amWhy
Aug 5 at 23:07





The question is about $left(-frac 12right)^4$. and $left(-frac 12right)^-4$
– amWhy
Aug 5 at 23:07













 

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