Integers are the set of numbers that include the negative numbers, positive numbers and zero. Integers cannot be fractions or decimals. One of the biggest challenges that students face when evaluating integers with exponents is when the number that is being raised to a power is negative.

What if the number is negative?

Example 1 : (-2)² = -2 •-2 = 4

Example 2 : (-3)³ = -3 •-3 •-3 = -27

Let's practice with variables.

Example 3 : if y = -3 find y² .

Substitute (-3) in for y. y² = (-3)²

Expand    y² = -3 •-3 = 9

Therefore y² = 9

Example 4 : find -x² when x = 7.

Substitute (7) in for x. -x² = - (7)²

Expand   -x² = -1 •7 •7 = -49

Therefore -x² = -49

Example 5 : find x⁵ if x = -5.

Substitute (-5) in for x. x⁵ = (-5)³

Expand    x⁵ = -5 •-5 •-5 •-5 •-5= -3125

Therefore x⁵ = -3125

Example 6: Compare (-4)² to -4²

(-4)² = (-4)(-4)=16 -4² =(-1)(4)(4) = 16

A few last reminders. It is usually best to put negative numbers in parentheses, especially if you are going to use the calculator to make your calculations. Remember that -x means (-1)x.

Related Links: Math algebra Exponents Exponents and Powers The Laws of Exponents Integers as Exponents Evaluate Exponents Positive and Negative Integer Exponents Rational (Fractional) Exponents Rational (Fractional) Exponents Zero Exponents Evaluate Cubes