You used the laws of exponents to find products and quotients of monomials.

LEQ: How do we evaluate and rewrite expressions involving rational exponents & solve equations involving expressions with rational exponents?

• rational exponent

• cube root

• nth root

• exponential equation

Radical and Exponential Forms

Answer:

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

= 9 Simplify.

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.

Answer:

Radical and Exponential Forms

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

Answer:

Radical and Exponential Forms

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

Answer:

Radical and Exponential Forms

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

Answer:

Radical and Exponential Forms

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

Answer:

Radical and Exponential Forms

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

Answer: 9

A. 16

B. 8

C. 4

D. 2

A. 16

B. 8

C. 4

D. 2

nth Roots

A.

Answer:

nth Roots

A.

Answer: 4

nth Roots

B.

Answer:

nth Roots

B.

Answer: 5

A. 343

B. 81

C. 49

D. 7

A. 343

B. 81

C. 49

D. 7

Evaluate b Expressions

Answer:

A.

= 11 Simplify.

Evaluate b Expressions

Answer: 11

A.

= 11 Simplify.

Evaluate b Expressions

Answer:

= 7 Simplify.

B.

Evaluate b Expressions

Answer: 7

= 7 Simplify.

B.

A. 4

B. 8

C. 16

D. 32

A. 4

B. 8

C. 16

D. 32

Evaluate b Expressions

Answer:

= 22 25 = 32

= 4 Simplify.

Evaluate b Expressions

Answer: 4

= 22 25 = 32

= 4 Simplify.

Evaluate b Expressions

Answer:

= 95 92 = 81

= 59,049 Simplify.

Evaluate b Expressions

Answer: 59,049

= 95 92 = 81

= 59,049 Simplify.

A. 216

B. 36

C. 18

D. 6

A. 216

B. 36

C. 18

D. 6

Solve Exponential Equations

A. Solve 9x = 729.

Answer:

9x = 729 Original equation

9x = 93 Rewrite 729 as 93.

x = 3 Power Property of equality

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 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.

A.

B.

C.

D. 2

Solve 93x + 1 = 274.

A.

B.

C.

D. 2

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:

Solve Exponential Equations

Rewrite 512 as 29.

72 = t Multiply each side by 8.

Power Property of Equality

Answer: 72

A. 6

B. 8

C. 9

D. 12

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.

A. 6

B. 8

C. 9

D. 12

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.