4-1 Exponents

4-1/4-2 Exponents and Integer Exponents

If a number is in exponential form, the exponent represents how many times the base is to be used as a factor. A number produced by raising a base to an exponent is called a power. Both 27 and 33 represent the same power.

7

ExponentBase

2

4-1 Exponents

Identify how many times 4 is a factor.4 • 4 • 4 • 4 = 44

Write in exponential form.

Example 1: Writing Exponents

A. 4 • 4 • 4 • 4

Read –(63) as “negative 6 to the 3rd power” or “negative 6 cubed”.

Reading Math

Identify how many times –6 is a factor.

(–6) • (–6) • (–6) = (–6)3

B. (–6) • (–6) • (–6)

4-1 Exponents

Identify how many times 5 and d are used as a factor.

Example 1: Writing Exponents

C. 5 • 5 • d • d • d • d

Write in exponential form.

5 • 5 • d • d • d • d = 52d4

4-1 Exponents

A. 35

= 243

35 = 3 • 3 • 3 • 3 • 3

Find the product of five 3’s.

Always use parentheses to raise a negative number to a power.

Helpful Hint

Simplify.Example 2: Simplifying Powers

4-1 Exponents

= 256

= (–4) • (–4) • (–4) • (–4) (–4)4

B. (–4)4

Simplify.

Example 2: Simplifying Powers

Find the product of four –4’s.

4-1 Exponents

Example 3: Using the Order of Operations

4(7) + 16

Substitute 4 for x, 2 for y, and 3 for z.

Evaluate the exponent.

Subtract inside the parentheses.

Multiply from left to right.

4(24 – 32) + 42

4(16 – 9) + 16

28 + 16

Evaluate x(yx – zy) + x for x = 4, y = 2, and z = 3.

y

x(yx – zy) + xy

Add. 44

4-1 Exponents

Look for a pattern in the table to extend what you know about exponents to include negative exponents.

÷ 10 ÷ 10 ÷ 10 ÷ 10

102 101 100 10–1 10–2

10 • 10

100

10

10 1

1 110

110

= 0.1

110 • 10

1100

= 0.01

4-1 Exponents

Example 1: Using a Pattern to Simplify Negative Exponents

Simplify. Write in decimal form.

A. 10–2

10–2 = 1

10 • 10

= 1100

= 0.01

B. 10–1

= = 0.1110

= 110

Extend the pattern from the table.

Multiply. Write as a decimal.

Extend the pattern from the table.

Multiply. Write as a decimal.

4-1 Exponents

4-1 Exponents

5–3

Write the power under 1; change the sign of the exponent.

Example 2: Evaluating Negative Exponents

Simplify.

Find the product of three ’s.1 5

Simplify.

4-1 Exponents

(–10)–3 Write the power under 1; change the sign of the exponent.

Additional Example 2: Evaluating Negative Exponents

Simplify.

Find the product of three ’s. 1 –10

Simplify.

1–10 • –10 • –10

–1000 1

= –0.001

4-1 Exponents

4–2

Write the reciprocal; change the sign of the exponent.

Example 3

Simplify.

Find the product of two ’s.1 4

Simplify.

41 2

14 • 4

161

4-1 Exponents

4-1 Exponents

Evaluate 82 –(11 – 20)–2.

Example 4: Zero Exponent Example