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
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