SOLUTION: why -2 to the power of 4 = -16?

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Question 1202091: why -2 to the power of 4 = -16?
Found 4 solutions by ikleyn, MathTherapy, math_tutor2020, greenestamps:
Answer by ikleyn(52787)   (Show Source): You can put this solution on YOUR website!
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why -2 to the power of 4 = -16?
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-2 to the power of 4 is not -16.

-2 to the power of 4 is 16.

= (-2)*(-2)*(-2)*(-2) = 16.         ANSWER



Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
why -2 to the power of 4 = - 16?

- 24 = (- 2)4 is NOT equal to - 16

However, it CAN BE if it's written a certain way. Can you determine that way?
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

It's a matter of order of operations (PEMDAS)

If we write (-2)^4, then
(-2)^4 = (-2)*(-2)*(-2)*(-2) = 16
The (-2)^4 means "multiply four copies of (-2) together to get 16"
The four negatives pair up and cancel out
negative * negative = positive

If on the other hand we have -(2^4), then,
-(2)^4 = -(2)*(2)*(2)*(2) = -16
The key difference this time is the negative doesn't get copied four times
We evaluate 2^4 first, then stick a negative at the front, to end up with -16.
Recall that PEMDAS has us do the parenthesis part first, then multiplication later. Think of -(2^4) as -1*(2^4)

Side note: many calculators will interpret -2^4 as -(2^4) and not as (-2)^4
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


When the expression is written in words, instead of with formal mathematical symbols, there are two different interpretations that give different answers.

(-2) to the power of 4 = (-2)^4 = 16

-(2 to the power of 4) = -(2^4) = -16
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