Introduction to Exponents Pre-Skills for 2.1

Basic Definitions Exponent: Tells how many times a base is used in a factor Base The number or variable that undergoes repeated multiplication Example 24 = 2 • 2 • 2 • 2 = 16

Important Examples -34 = - (3 • 3 • 3 • 3) -1 (9 • 9 ) = -81 (-3)4 = - (3 • 3 • 3 • 3) -1 (9 • 9 ) = -81 (-3)4 = -3 • -3 • -3 • -3 = 9 • 9 = 81 -33 = - (3 • 3 • 3 ) -1 (27) = -27 (-3)3 = -3 • -3 • -3 = 9 • -3 = -27 x5 = x • x • x • x • x y3= y • y • y

Reminders on Evaluating Exponents A base with an exponent of zero equals 1 10 0 = 1 25,000 0 =1 A base with an exponent of 1 equals the base 51 = 5 1,000 1 =1,000

Reminders A positive base with a even exponent equals a positive answer Example 52= 5 • 5 = 25 A negative base with an even exponent equals a positive answer: Example: (-3)2 = (-3) • (-3) = 9 A negative with an odd exponent equals a negative answer Example: (-2)3= (-2)(-2)(-2) = -8 A base with a negative sign in front equals a negative answer Example: -23= -(2 • 2 • 2) = -8 Example: -92= - (9 •9)= -81

Exponents with Fractions

When exponents are on fractions The fraction is the base Write out the fraction as many times as decided by the exponent Multiply the numerator Multiply the denominator Final answer

example ( 2 3 )2 Write out the fraction twice 2 3 x 2 3 Multiply the numerator 2 x 2 = 4 Multiply the denominator 3 x 3 =9 Final Answer= 4 9

example ( 1 2 )4 Write out the fraction four times 1 2 x 1 2 x 1 2 x 1 2 Multiply the numerator 1 x 1 x 1 x 1 =1 Multiply the denominator 2 x 2 x 2 x 2 = 16 Final Answer= 1 16