Over Lesson 7–2

Rational Exponents

Lesson 7-3

Understand how to rewrite and evaluate expressions involving rational exponents and solve equations containing rational expressions.

LEARNING GOAL

VOCABULARY

Radical and Exponential Forms

Answer: 9

Write each expression in radical form, or write each radical in exponential form.

= 9 Simplify.

Radical and Exponential Forms

Write each expression in radical form, or write each radical in exponential form.

nth Roots

A.

B.

C.

Evaluate b Expressions

Answer: 11

A.

= 11 Simplify.

Evaluate b Expressions

Answer: 7

= 7 Simplify.

B.

Evaluate b Expressions

Answer: 4

= 22 25 = 32

= 4 Simplify.

Evaluate b Expressions

Answer: 59,049

= 95 92 = 81

= 59,049 Simplify.

Solve Exponential Equations

A. Solve 9x = 729.

Answer: 3

9x = 729 Original equation

9x = 93 Rewrite 729 as 93.

x = 3 Power Property of equality

Solve Exponential Equations

B. Solve 162x – 1 = 8.

162x – 1 = 8 Original equation

(24)2x – 1 = 23 Rewrite 16 as 24 and 8 as 23.

28x – 4 = 23 Power of a Power, Distributive Property

8x – 4 = 3 Power Property of Equality

8x = 7 Add 4 to each side.Divide each side by 8.

Answer:

Solve 93x + 1 = 274.

BIOLOGY The population p of a culture that begins

with 40 bacteria and doubles every 8 hours can be

modeled by , where t is time in hours. Find

t if p = 20,480.

Original equation

p = 20,480

Divide each side by 40.

Solve Exponential Equations

Solve Exponential Equations

Rewrite 512 as 29.

72 = t Multiply each side by 8.

Power Property of Equality

Answer: 72

NEWS The number of hits to a news story online

can be modeled by , where t is time in

hours. Find t if h = 24,576.

Homework

p