Warm Up

A. Powers

A power indicates how many times a number is to be multiplied by itself. The number of times a number is to be multiplied by itself is known as an exponent or an index. For instance, 4 to the power of 3 is the number four multiplied by itself three times, 4 3 = 4 × 4 × 4.



Powers
indicate how many times a number is to be multiplied by itself. The base represents the number, and the index (or the exponent) is the number of times the base is multiplied by itself.


The power 42 is commonly read as

  • four to the exponent two, or

  • four to the power of two, or

  • four squared - "squared" is reserved for when the index (or exponent) is 2.


Exponent
a superscripted number on the base of a power that represents how many times the base number is multiplied by itself


The following example demonstrates how to translate, expand, and evaluate what a power represents.

Example 1

Given the power 63,

  • rewrite the power in words,

  • expand the power, and

  • evaluate the power.

63: six to the exponent three, six to the power of three, or six cubed
6 3 = 6 × 6 × 6
6 3 = 216

Sometimes brackets are used when evaluating powers. The placement of a negative sign, in relation to the brackets, can influence the value of a power. Consider the following examples.

  • 72 = 7 × 7 = 49

  • (−7)2 = −7 × −7 = 49

  • −72 = −(7 × 7) = −49