1. Warm Up Simplify. 1.-20 ÷ (2) 2. (–2)(–2) 3. (–2)(–2)(–2) 4. -3(3)(-3) -10 4 –8 27 4949 5.

2. Section 1.4 Powers and Exponents

3. 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)

4. 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.

5. 2 3 = 2 2 2 = 8

6. 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  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 3 9 27 81 243 3131 3232 3 3434 3535 Reading Exponents

7. Reading a Power PowerVerbal PhraseRepeated Multiplication

8. 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.

9. Rewrite each power as repeated multiplication and evaluate 4 2 = 3 4 = 10 3 = 4 4 = 16 3 3 3 3 = 81 10 10 10 = 1000

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

11. 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 = 3 3 3 V = 27 units

12. Simplify the following if x = 4 x 2 = 2 x = x 2 x = 4 2 = 4 4 = 16 2424 = 2 2 2 2 = 16 4 2 4= 16 4 = 64

13. Use as a factor 2 times. 2 92 9 Simplify the expression. 2929  2929 Evaluating Powers = 4 81 2929  2929

14. 1. Write the power represented by the geometric model. n n n2n2 Simplify each expression. 2. 4. 6 3. –6 3 5. (–2) 6 −216 21664 Lesson Quiz Write each number as a power of the given base. 6. 343; base 77. 10,000; base 107373 10 4