Warm Up Simplify ÷ (2) 2. (–2)(–2) 3. (–2)(–2)(–2) 4. -3(3)(-3) –

Section 1.4 Powers and Exponents

Objectives Interpret and evaluate expressions involving powers. (AF2.0) Interpret positive whole number powers as repeated multiplication. (AF2.1) Use formulas for finding the area and volume of basic figures. (MG2.1)

Words to Know Power –an expression written with an exponent and a base or the value of such an expression. 3² is an example of a power. Base –The base, 3, is the number that is used as a factor. Exponent –The exponent, 2, tells how many times the base, 3, is used as a factor.

2 3 = = 8

3 to the second power, or 3 squared 3  3  3  3  3 Multiplication Power Value Words 3  3  3  3 3  3  3 3  to the first power 3 to the third power, or 3 cubed 3 to the fourth power 3 to the fifth power Reading Exponents

Reading a Power PowerVerbal PhraseRepeated Multiplication

Caution! In the expression –5², 5 is the base because the negative sign is not in parentheses. In the expression (–2)³, –2 is the base because of the parentheses.

Rewrite each power as repeated multiplication and evaluate 4 2 = 3 4 = 10 3 = 4 4 = = = 1000

Now you try… 2 9 = 3 4 = 7 3 = 5 4 = 8 3 = 10 5 =

Area and Volume AREA of a SQUARE A = s 2 A = 3 2 A = 3 3 A = 9 units Volume of a Cube V = s 3 V = 3 3 V = V = 27 units

Simplify the following if x = 4 x 2 = 2 x = x 2 x = 4 2 = 4 4 = = = = 16 4 = 64

Use as a factor 2 times Simplify the expression  2929 Evaluating Powers =  2929

1. Write the power represented by the geometric model. n n n2n2 Simplify each expression  3. – (–2) 6 − Lesson Quiz Write each number as a power of the given base ; base ,000; base