Multiplication Properties of Exponents WarmUp Find the value
- Slides: 14
Multiplication Properties of Exponents
Warm-Up Find the value of each. 1. 42 16 2. 53 125 3. (2 − 9)2 4. 3(2 + 4)2 + 12 49 109
Powers, Bases and Exponents Exponent Base 4 3 =3 3 Expanded Form Power Read as “ 3 to the 4 th power”
Vocabulary Power An expression such as xa which consists of two parts, the base (x) and the exponent (a). Base The base of the power is the repeated factor. In xa, x is the base. Exponent In xa, a is the exponent. The exponent shows the number of times the factor (x) is repeated. Squared A term raised to the power of 2. Cubed A term raised to the power of 3.
Write each expression in EXPANDED FORM. Then, write as a SINGLE BASE AND EXPONENT. a. 53 • 54 What is the rule? b. 42 • 48 c. x 3 • x 2
Write each of the following expressions as a single term. a. b.
Multiplication Properties of Exponents Product of Powers To multiply two powers with the same base, add the exponents. Power of a Power To find the power of a power, multiply the exponents. Power of a Product To find the power of a product, find the power of each factor and multiply.
Example 1 Simplify the following. a. y 3 x 2 y 6 x Group like variables together. Add exponents with the same base.
Example 1 Continued… Simplify the following. b. (b 3 w 2)4 Distribute the exponent to each base. Multiply exponents.
Example 1 Continued… Simplify the following. c. (5 p 4)(2 p 3) Group like values together. Multiply coefficients. Add exponents with the same base.
Good to Know! A simplified expression should have: each base appear exactly once, no powers to powers, no numeric values with powers, and fractions written in simplest form.
Example 2 Simplify the following. a. 6 x 2 y 4 z 3 ∙ 3 x 5 z 2 Group like terms together. Multiply coefficients. Add exponents with the same base.
Example 2 Continued… Simplify the following. b. (4 m 3 w)2(5 m 2 w 2)3 Distribute the exponent to each base. 42(m 3)2(w)2 ∙ 53(m 2)3(w 2)3 Evaluate coefficients and multiply exponents. 16 m 6 w 2 ∙ 125 m 6 w 6 Multiply coefficients. Add exponents with the same base. (16 ∙ 125) ∙ m 6 m 6 w 2 w 6 2000 m 12 w 8
CH 3 Formative 1 Simplify. 1. y 4 y 6 y 10 4. (4 x 5 y)(3 x 2 y 2) 12 x 7 y 3 2. (p 3)2 3. (5 w)2 p 6 25 w 2 5. (2 x 2)4(3 x 3)2 144 x 14