Exponential doubt

Question

What is the value of

-2^4

is it -16 or 16

as -2^4 can be (-1) * 2^4 = - 16

-2^4 can also be -2 * -2 * -2 * -2 = +ve 16

which is right i am puzzled

fluke · Answer

The way it is written, it should be -16 
-2^4=-1*2^4=-1*2*2*2*2=-1*16=-16

(-2)^4=-2*-2*-2*-2=+16

GMAT generally doesn't create such confusion. Is there any question that you found ambiguous?

pike · Answer

The only place this will be ambiguous is on poorly written questions or on questions transcribed to forums wrong. Real GMAT questions will be clear.

Shoumik · Answer

(-2) ^ 4 = +16

- (2)^4 = -16.

The difference between the above two expressions is that the negative sign is inside the parenthesis in the first expression and outside the parenthesis in the second expression.

1st expression can also be written as  (-1)^4  *  (2)^4  =  1   *  16  =  +16 
2nd expression can be written as: (-1)^1 * (2)^4 = (-1) * (16) =  -16

In the second expression, the exponent 4 ONLY APPLIES TO '2' not '-2' since there aren't any parenthesis around the whole expression. You have to assume the exponent only applies to the number '2' and not '-2'.

Notice that the second expression is negative because the negative sign is outside of the parenthesis and the positive exponent (in this case, 4) doesn't affect it whereas in the first expression the positive exponent 4 DOES affect it.

However, if you have an ODD EXPONENT, then it does not matter, the final answer will always be negative. For example:

(-2) ^ 3 = (-2) (-2) (-2) = -8
- 2^3 = (-1)^1 (2*2*2) = -8.

But it is still recommended that you USE PARENTHESIS just to make life easier and questions less complicated for you.

Exponential doubt

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