1. L7-4 Obj: Students will simplify expressions with rational exponents
Students will convert to and from radical form

2. Definition: Rational Exponents

4. Properties of Exponents
Product of Powers – when multiplying the bases – add the powers
Power of a power – multiply the powers
Power of a product – distribute the power

5. Properties of Exponents
Quotient of powers – when dividing the bases – subtract the exponents
Power of a quotient – distribute the power
Zero product property – anything to the zero power =1

6. Negative Exponents

7. Simplify each expression.
Rational Exponents
LESSON 7-4
Additional Examples
Simplify each expression.
a. 64 1 3
b. 7 • 7 1 2

8. c. 5 • 25 (continued) 1 3 Rational Exponents Additional Examples
LESSON 7-4
Additional Examples
(continued)
c. 5 • 25 1 3

9. a. Write the exponential expressions x and y –0.4 in radical form.
Rational Exponents
LESSON 7-4
Additional Examples 2 7
a. Write the exponential expressions x and y –0.4 in radical form.
b. Write the radical expressions and in exponential form. 4 c3 3
b 5

10. It would take 4.15 hours to cook a 13 pound pot roast.
Rational Exponents
LESSON 7-4
Additional Examples
The time t in hours needed to cook a pot roast that weighs p pounds can be approximated by using the equation t = 0.89p0.6. To the nearest hundredth of an hour, how long would it take to cook a pot roast that weighs 13 pounds?
t = 0.89p0.6 Write the formula.
= 0.89(13)0.6 Substitute for p.
4.15 Use a calculator.
It would take 4.15 hours to cook a 13 pound pot roast.

11. Simplify each number. a. (–27) 2 3 Rational Exponents
LESSON 7-4
Additional Examples
Simplify each number.
a. (–27) 2 3

12. b. 25–2.5 (continued) Rational Exponents Additional Examples
LESSON 7-4
Additional Examples
(continued)
b. 25–2.5

13. Write (243a–10) in simplest form.
Rational Exponents
LESSON 7-4
Additional Examples
Write (243a–10) in simplest form. 2 5

15. Practice (on your whiteboards)

20. L7.4 (p 394) #34-56e 65-70a