Ch 8: Exponents A) Product & Power Properties Objective: To recognize the properties of exponents and use them to simplify expressions.

x 3 x x x = exponent base Base The foundation of an expression that is raised to a power is known as the base. Exponent An exponent represents the number of times an expression is multiplied by itself and is written in superscript. Definitions

n n n n x a = x b x a + b n 3 = n 2 n Example: = n 5 n 5 1)Expand the bases as many times as the exponents states. 2)Count the number of times the variable appears – that is the exponent. Shortcut: Evaluate the bases separately and ADD the exponents. Product Property Rules

Example 1Example 2 Example 3Example 4 xx x 2  x 3 xxx = x5x5 2xx 2x 2  3x 3 3xxx = 6x 5 2x2x (2x) 2  3x 3 3xxx = 12x 5 2xyy 2xy 2  − 3x 3 y 3xxxy = − 6x 4 y 3 223223 xxxxx 12x5x5 2−32−3 xxxx −6−6x4x4 yyy y3y3

Classwork 1) 2) 3) 4) 5) 6) 2 xxx 4 xxxxx = 8x 8 -3 nnnnnnn 2nn = -6n 9 -3 aaaa -2aa = 6a 6

Example: 1)Expand the base (whatever is inside the parenthesis) as many times as the exponent states. 2)Continue expanding until there are no more exponents. 3)Count the number of times the variable appears – that is the exponent. Shortcut: MULTIPLY the exponents. ( ) x a = b x abab n 3 (n )  (n ) 3 = n 3232 n  n  n  n  n  n = n Power to Power Property Rules

Example 5Example 6 Example 7Example 8 xx (x 2 ) 3 xx = x6x6 2xx (2x 2 ) 3 2xx = 8x 6 xx2xx 222222 xxxxxx - 2xx (-2x 2 ) 3 - 2xx = - 8x 6 - 2xx -2-2-2-2-2-2 xxxxxx 2xxy (2x 2 y) 3 2xxy = 8x 6 y 3 2xxy 222222 xxxxxxyyy

Classwork 1) 3) 2) 4) 5) 6)