Powers: Even and Odd Powers - Effect on Sign

Which is greater, -256² or (-256)²?

Incorrect.

They most certainly are NOT.

Correct.

There's no need to calculate 256² to answer this question - just follow the rules for power sign we've just learned. Consider each expression individually.

-256²:  since the negative sign is not included in the base, first apply the exponent, then the negative sign. 256² is positive; applying the negative sign afterwards creates a negative result.

(-256)²: Since the negative sign is inside the parentheses, it is included in the base. Since an even power is always positive (regardless if the base is positive or negative), (-256)² gives a positive result.

Therefore, (-256)² > 0 > -256².

Some GMAT questions test your understanding of Even and Odd exponents, and their effects on the expression sign (positive or negative).

Remember this difference between even and odd powers:

An even power is always positive, whether the base is positive or negative.

2⁴ is positive = 16.

(-2)⁴ is also positive. Even though the base is negative, (-2)⁴ = (-2)·(-2)·(-2)·(-2) = 16. Remember: any pair of minus times minus become plus.

An odd power retains the base's original sign. 

If the base is positive, raising it to an odd power will give a positive result as well. e.g. 2³ = +8

if the base is negative, raising it to an odd power will give a negative result. e.g. (-2)³ = (-2)·(-2)·(-2) = -8

Note that whether the minus sign is inside or outside the parentheses is important!

(-2)⁴ means that the minus sign is part of the base and is affected by the exponent. e.g. (-2)⁴ = (-2)·(-2)·(-2)·(-2) = 16

-2⁴ means that the minus sign is not part of the base - First apply the power, then apply the minus sign. In this case, -2⁴ = -(2·2·2·2) = -(16) = -16.

-256²

(-256)²