1. Ch. 7.4 Rational Exponents p. 379

2. Rational Exponents If the nth root of a is a real number and m is an integer, then: and If m is negative, a ≠ 0

3. Rational Exponents ALGEBRA 2 LESSON 7-4 Simplify each expression. 3 = 4 3 Rewrite 64 as a cube. = 4Definition of cube root. a.64 1313 3 64 = 64 Rewrite as a radical. 1313 = 7By definition, 7 is the number whose square is 7. b.7 7 1212 1212 7 7 = 7 7 Rewrite as radicals. 1212 1212 7-4

4. Rational Exponents ALGEBRA 2 LESSON 7-4 (continued) c.5 25 1313 1313 5 25 = 5 25Rewrite as radicals. 1313 1313 33 3 = 5 25 property for multiplying radical expressions 7-4 = 5By definition, 5 is the number whose cube is 5. 3

5. Check Understanding P. 379 Check understanding # 1 A - C

6. Properties of Rational Exponents Let m and n represent rational numbers. Assume that no denominator equals 0. Property Example

7. Properties of Rational Exponents Continued PropertyExample

8. Rational Exponents ALGEBRA 2 LESSON 7-4 a.Write x and y –0.4 in radical form. 2727 y –0.4 = y = or 2525 – 1y21y2 5 1 y 2 5 b.Write the radical expressions and in exponential form. c3c3 4 b 5 3 = c 3434 c3c3 4 b 5 3 = b 5353 7-4 2727 x = x 2 or x 2 7 7

9. Check Understanding p. 380, Check Understanding 2 A & B

10. Rational Exponents ALGEBRA 2 LESSON 7-4 Simplify each number. a.(–27) 2323 Method 1 = (–3) 2 = 9 (–27) = ((–3) 3 ) 2323 2323 Method 2 3 = ( (–3) 3 ) 2 = (–3) 2 = 9 3 (–27) = ( –27) 2 2323 7-4

11. Rational Exponents ALGEBRA 2 LESSON 7-4 (continued) b.25 –2.5 Method 1 25 –2.5 = 25 5252 – = (5 2 ) 5252 – = 5 2 5252 – = 5 –5 = 1551555 = 1 3125 Method 2 25 –2.5 = 25 5252 – 1 25 5252 = = 1551555 1 3125 = = 1 ( 25) 5 7-4

12. Check Understanding P. 381, Check understanding #4 A - C

13. Rational Exponents ALGEBRA 2 LESSON 7-4 Write (243a –10 ) in simplest form. = 3 2 a –4 2525 (243a –10 ) = (3 5 a –10 ) 2525 2525 = 3 5 a (–10) 2525 2525 32a432a4 = = 9a49a4 7-4

14. Check Understanding P. 382, Check Understanding # 5

15. Homework Page 382 # 2 – 22 eoe, 30 – 60 eoe