Integer Exponents CA 2.0

Objective - To solve problems involving negative exponents and zero exponents.

Bases and Exponents x x ∙ x ∙ x = exponent base 3 x x ∙ x ∙ x = base The BASE tells us what is being multiplied. The EXPONENT tells us how many times to multiply the base.

Identifying the Base & Exponent The base is 5. The exponent is 2. The base is 5. The exponent is 2. The base is - 5. The exponent is 2. The base is (x + 5). The exponent is 2.

Evaluating Exponents

Simple Rule Example: If the base is negative: An even exponent means a positive answer An odd exponent means a negative answer Example:

For all real numbers x, x ≠ 0, and n is an integer: Negative Exponents For all real numbers x, x ≠ 0, and n is an integer:

Working with Negative Exponents When you see a negative exponent, think FRACTION! If no fraction exists, create a fraction, by putting what you have over 1! Examples:

Fractions As Bases If you have a fraction as the base, and there is a negative exponent: FLIP THE FRACTION! Example:

Simplify. 1) 3) 5) 2) 4) 6)

Follow the Pattern! = 3 3 3 = 3 3 = 3 = 1 = = =

3 3 3 3 1 Simplify. 1 Factor Explanation Negative Exponent Explanation 2 -2 2 + -2 3 3 = 3 = 3 = 1 9 9 = 1 For all real numbers x, x ≠ 0,

Negative Exponents in Denominator Evaluate. Simplify. 1) 3) 2) 4)

Examples:

x x x 3 3 3 3 9 Negative exponents follow rules of exponents. = = = = Rule of Common Bases a a + b x x b x = 3 4 4 + -2 3 -2 3 3 2 9 = = = 81 81 = 9

( ) ( ) ( ) x x 2 2 2 8 Negative exponents follow rules of exponents. Power to Power Rule ( ) b a ab x x = -2 ( ) 3 3(-2) -6 2 2 2 = = = = -2 ( ) 8 = =

Simplify. 1) 4) 2) 5) 3) 6)

Simplify. 1) 4) 2) 5) 3) 6)