By Avramov L.L. (ed.), Tchakerian K.B. (ed.)

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The expression is read as “four to the third power” The base (4) is multiplied by itself as many times as the power requires (3). Thus, 43 = 4 x 4 x 4 = 64. Thus, exponents are actually shorthand for repeated multiplication. Two exponents have special names: the exponent 2 is called the square, and the exponent 3 is called the cube. 52 can be read as five squared (52 = 5 x 5 = 25). 53 can be read as five cubed (53 = 5 x 5 x 5 = 125). All About the Base________________________ A Variable Base Variables can also be raised to an exponent, and behave the same as numbers.

One-Solution Quadratics Not all quadratic equations have two solutions. Some have only one solution. One-solution quadrat­ ics are also called perfect square quadratics, because both roots are the same. Consider the following examples: x1+ Sx + 16 = 0 (x + 4)(x + 4) = 0 (x + 4 )2 = 0 Here, the only solution for x is -4 . x2- 6 x + 9 = 0 (x -3 )(x -3 ) = 0 Here, the only solution for x is 3. ( x - 3 ) 2= 0 Be careful not to assume that a quadratic equation always has two solutions. Always factor quadratic equations to determine their solutions.

52 can be read as five squared (52 = 5 x 5 = 25). 53 can be read as five cubed (53 = 5 x 5 x 5 = 125). All About the Base________________________ A Variable Base Variables can also be raised to an exponent, and behave the same as numbers. yA= y X y X y X y Base of 0 or 1 0 raised to any power equals 0 1 raised to any power equals 1 For example, 03 = 0 x 0 x 0 = 0 and 04 = 0 x 0 x 0 x 0 = 0. 37 Chapter 3 Exponents Similarly, 13 = 1 x 1 x 1 = 1 and 14 = 1 x 1 x 1 x 1 = 1, Thus, if you are told that x = x 2, you know that # must be either 0 or 1.

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