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Apply Exponent Properties Involving Products USE PROPERTIES OF EXPONENTS INVOLVING PRODUCTS REMEMBER: EXPONENTS LOOK LIKE THIS: x3 PRODUCTS INVOLVE MULTIPLICATION! (x) Prerequisite Skills VOCABULARY CHECK 1. Identify the exponent and the base in the expression 138. ANSWER Exponent: 8, base: 13 2. Copy and complete: An expression that represents repeated multiplication of the same factor is called a(n) ? . ANSWER Power Prerequisite Skills SKILLS CHECK Evaluate the expression. 3. x2 when x = 10 4. a3 when a = 3 ANSWER ANSWER 27 100 5 1 2 3 5. r when r = 6. z when z = 6 2 ANSWER ANSWER 25 36 1 8 Prerequisite Skills SKILLS CHECK Order the numbers from least to greatest. 7. 6.12, 6.2, 6.01 8. 0.073, 0.101, 0.0098 ANSWER ANSWER 6.01, 6.12, 6.2 0.0098, 0.073, 0.101 Write the percent as a decimal. 9. 4% 10. 0.5% 11. 13.8% 12. 145% ANSWER ANSWER ANSWER ANSWER 1.45 0.04 0.005 0.138 Prerequisite SkillsSKILLS CHECK 13. Write a rule for the function. ANSWER f (x) = x + 2 Use the product of powers EXAMPLE 1 property 8 3 5 3 + 5 a. 7 7 = 7 =7 8 2 1 8 2 b. 9 9 9 = 9 9 9 1+8+2 c. d. =9 11 =9 6 (– 5)(– 5) = (– 5)1 (– 5)6 1+6 = (– 5) 7 = (–5) 4 3 4+3 7 x x =x =x for Example 1 GUIDED PRACTICE Simplify the expression. 2 7 9 3 3 =3 1. 9 10 2. 5 5= 5 2 3 3.(– 7) (– 7) = (–7) 4. x2 x6 x = x9 EXAMPLEUse 2 the power of a power property a . (25)3 = 25 c. (x2)4 3 = 215 = x2 = x8 b. [(–6)2]5= (–6)2 5 = (–6)10 4 6]2 [(y + 2) d. = (y + 2)6 = (y + 2)12 2 for Example 2 GUIDED PRACTICE Simplify the expression. 5. (42)7= 414 7. 3 6 (n ) = 6. [(–2)4]5 = (–2)20 18 n 8. [(m + 1)5]4 = (m + 1)20 Use the power of a product EXAMPLE 3 property a. (24 13)8 = 248 138 b. (9xy)2 = (9 x y)2 = 92 x2 y2 = 81x2y2 c. (–4z)2 = (–4 z)2 = (–4)2 z2 = 16z2 d.– (4z)2 = – (4 z)2 = – (42 z2) = –16z2 Use all three properties EXAMPLE 4 Simplify (2x3)2 x4 (2x3)2 x4 = 22 (x3)2 x4 Power of a product property = 4 x6 x4 Power of a power property 10 = 4x Product of powers property for Examples 3, 4 GUIDED PRACTICE and 5 Simplify the expression. 9. (42 12)2 = 422 122 2 2 = 9n (–3n) 10. 11. (9m3n)4 = 6561m12n4 12. 5 (5x2)4 = 3125x8 Success Criteria: I can now: Use all three product properties when multiplying with exponents