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Evaluating Exponents of Negative Numbers

An exponent is a number that tells how many times the base number is used as a factor. For example, 34 indicates that the base number 3 is used as a factor 4 times. To determine the value of 34, multiply 3*3*3*3 which would give the result 81.

If a negative number is raised to an even power, the result will be positive.
(-2)4 = -2 * -2 * -2 * -2 = 16
If a negative number is raised to an odd power, the result will be negative.
(-2)5 = -2 * -2 * -2 * -2 * -2 = -32

The negative number must be enclosed by parentheses to have the exponent apply to the negative term.
Note that (-2)4 = -2 * -2 * -2 * -2 = 16
and -24 = -(2 * 2 * 2 * 2) = -16

Exponents are written as a superscript number (e.g. 34) or preceded by the caret (^) symbol (e.g. 3^4).

Some facts about exponents:

  • Zero raised to any power is zero (e.g. 05 = 0)
  • One raised to any power is one (e.g. 15 = 1)
  • Any number raised to the zero power is one (e.g. 70 = 1)
  • Any number raised to the first power is that number (e.g. 71 = 7)





Practice

Determine the value of each exponential expression

 
 
 =   

 


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