Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Why is $(-3)^4 =81$ and $-3^4 =-81 $?This might be the most stupidest question that you might have encountered,but unfortunately i'am unable to understand this.

share|improve this question
add comment

4 Answers

up vote 3 down vote accepted

By definition

$(-3)^4 = (-3)\cdot(-3)\cdot(-3)\cdot(-3) = 9\cdot 9 = 81$

$-3^4 = -(3^4) = -(3\cdot 3\cdot 3\cdot 3) = - 81$

share|improve this answer
add comment

Note that $(-3)^4=((-1)\cdot3)^4=(-1)^4\cdot3^4=81$

Again note that $-3^4=(-1)\cdot3^4=-81$

share|improve this answer
and then we understand the difference between $(-1)^4$ and $-1^4$. –  Parth Kohli Jan 24 '13 at 10:12
@Novice: I think OP need to understand this fact that you are given. –  A.D Jan 24 '13 at 10:13
add comment

$$(-3)^4 = -3 \cdot -3\cdot -3\cdot -3 = 9\cdot9=81 $$Now, when we have to "simplify" the expression $-3^4$, first we do the exponent and then the rest. So this simplifies to $-(81) = -81$

This question had confused me a lot too, and then I got my enlightenment (now waiting for the badge)...

share|improve this answer
Good Refresher Isn't it! +1 for you too! –  alok Jan 24 '13 at 10:24
add comment

Because multiplication doesn't distribute into exponentiation. That is, $a(b^c) = (ab)^c$ doesn't always hold. And there's no reason why it should, unless $c = 1$. So $(-3)^4 = (-1 \cdot3)^4 = (-1)^4 \cdot (3)^4 = 81$, and not $-81$, as the multiple of $-1$ doesn't factor out.

share|improve this answer
add comment

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.