Evaluate integers with exponents.

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


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