Lesson Menu Main Idea Key Concept:Negative Exponents Example 1:Use Positive Exponents Example 2:Use...

Main Idea

Key Concept: Negative Exponents

Example 1: Use Positive Exponents

Example 2: Use Positive Exponents

Example 3: Use Negative Exponents

Example 4: Use Negative Exponents

Example 5: Perform Operations with Exponents

Example 6: Perform Operations with Exponents

Example 7: Real-World Example

• Write expressions using negative exponents.

Use Positive Exponents

Write 7

–4 using a positive exponent.

Definition of a negative exponent

Answer:

Write 3

–3 using a positive exponent.

A.

B.

C.

D.

Write y

–8 using a positive exponent.

Use Positive Exponents

Definition of a negative exponent

Answer:

Write x

–4 using a positive exponent.

A.

B.

C.

D.

Use Negative Exponents

Write using a negative exponent.

Definition of exponent

= 10

–2 Definition of a negative exponent

Answer: 10

–2

A. 4–2

B. 2–4

C. 2–3

D. 2–2

Write using a negative exponent.

Use Negative Exponents

Write using a negative exponent.

Definition of exponent

= m

–9 Definition of a negative exponent

Answer: m

–9

A. x

–5

B. –x

–5

C. x

–6

D. –x

–6

Write using a negative exponent.

Perform Operations with Exponents

Simplify x

5 • x

–8.

Method 1 Quotient of Powers

x

5 • x

–8 = x

5 + (–8)

= x–

3

Perform Operations with Exponents

Answer: x

–3

Method 2 Definition of Power

A. y

–26

B. y

–6

C. y

26

D. y

6

Simplify y

10 • y

–16.

Perform Operations with Exponents

Simplify .

Method 1 Quotient of Powers

= d

3

Perform Operations with Exponents

Answer: d

3

Method 2 Definition of Power

A. r

B. r

7

C. r –1

D. –r –7

Simplify .

WAVELENGTHS Nanometers are often used to measure wavelengths. 1 nanometer = 0.000000001 meter. Write the decimal as a power of 10.

The digit 1 is in the billionths place.

Write the decimal as a fraction.

1,000,000,000 = 109

Definition of a negative exponent

Answer: A nanometer is 10

–9 meter.

A. 10

–10 meter

B. 10

–11 meter

C. 10

–12 meter

D. 10

–15 meter

A picometer is a unit of measurement that is even smaller than a nanometer. 1 picometer = 0.000000000001 meter. Write the decimal as a power of 10.