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4-1
4-1 Exponents
Exponents
Warm Up
Problem of the Day
Lesson Presentation
Course
Course
33
4-1 Exponents
Warm Up
Find the product.
1. 5 • 5 • 5 • 5
625
2. 3 • 3 • 3
27
3. (–7) • (–7) • (–7) –343
4. 9 • 9
Course 3
81
4-1 Exponents
Problem of the Day
What two positive integers when
multiplied together also equal the sum
of the same two numbers?
2 and 2
Course 3
4-1 Exponents
Learn to evaluate expressions with
exponents.
Course 3
4-1 Exponents
Vocabulary
exponential form
exponent
base
power
Course 3
4-1 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.
Exponent
Base
2
Course 3
7
4-1 Exponents
Additional Example 1: Writing Exponents
Write in exponential form.
A. 4 • 4 • 4 • 4
4 • 4 • 4 • 4 = 44
Identify how many
times 4 is a factor.
B. (–6) • (–6) • (–6)
(–6) • (–6) • (–6) =
(–6)3
Identify how many
times –6 is a factor.
Reading Math
Read –(63) as “-6 to the 3rd power or -6
cubed”.
Course 3
4-1 Exponents
Additional Example 1: Writing Exponents
Write in exponential form.
C. 5 • 5 • d • d • d • d
5 • 5 = 52d4
Course 3
Identify how many
times 5 and d are
used as a factor.
4-1 Exponents
Check It Out: Example 1
Write in exponential form.
A. x • x • x • x • x
x • x • x • x • x = x5
Identify how many
times x is a factor.
B. d • d • d
d • d • d = d3
Course 3
Identify how many
times d is a factor.
4-1 Exponents
Check it Out: Example 1
Write in exponential form.
C. 7 • 7 • b • b
2
2
7•7=7 b
Course 3
Identify how many times 7
and b are used as a factor.
4-1 Exponents
Additional Example 2: Evaluating Powers
Evaluate.
Find the product of five 3’s.
A. 35
35 = 3 • 3 • 3 • 3 • 3
= 243
B. (–3)5
Find the product of five –3’s.
(–3)5 = (–3) • (–3) • (–3) • (–3) • (–3)
= –243
Helpful Hint
Always use parentheses to raise a negative number
to a power.
Course 3
4-1 Exponents
Additional Example 2: Evaluating Powers
Evaluate.
C. (–4)4
(–4)4= (–4) • (–4) • (–4) • (–4)
= 256
D. 28
28 = 2 • 2 • 2 • 2 • 2 • 2 • 2 • 2
= 256
Course 3
Find the product
of four –4’s.
Find the
product of eight
2’s.
4-1 Exponents
Check It Out: Example 2
Evaluate.
Find the product of four 7’s.
A. 74
74 = 7 • 7 • 7 • 7
= 2401
B. (–9)3
Find the product of three –9’s.
(–9)3 = (–9) • (–9) • (–9)
= –729
Course 3
4-1 Exponents
Check It Out: Example 2
Evaluate.
C. –(5)2
–(5)2 = –(5) • (5)
= –25
D. 97
97 = 9 • 9 • 9 • 9 • 9 • 9 • 9
= 4,782,969
Course 3
Find the product of
two 5’s and then
make the answer
negative.
Find the product of
seven 9’s.
4-1 Exponents
Additional Example 3: Using the Order of Operations
Evaluate x(yx – zy) + xy for x = 4, y = 2,
and z = 3.
x(yx – zy) + xy
= 4(24 – 32) + 42
Substitute 4 for x, 2 for y,
and 3 for z.
= 4(16 – 9) + 16
Evaluate the exponent.
= 4(7) + 16
Subtract inside the parentheses.
= 28 + 16
Multiply from left to right.
= 44
Add.
Course 3
4-1 Exponents
Check It Out: Example 3
Evaluate z – 7(2x – xy) for x = 5, y = 2,
and z = 60.
z – 7(2x – xy)
= 60 – 7(25 – 52)
Substitute 5 for x, 2 for y,
and 60 for z.
= 60 – 7(32 – 25) Evaluate the exponent.
= 60 – 7(7)
Subtract inside the parentheses.
= 60 – 49
Multiply from left to right.
= 11
Subtract.
Course 3
4-1 Exponents
Additional Example 4: Geometry Application
1
Use the formula 2 (n2 – 3n) to find the number
of diagonals in a 7-sided figure.
1
2
1
2
1
2
1
2
1
2
(n2 – 3n)
(72 – 3 • 7) Substitute the number of sides for n.
(49 – 3 • 7) Evaluate the exponent.
(49 – 21)
Multiply inside the parentheses.
(28)
Subtract inside the parentheses.
14 diagonals
Course 3
Multiply
4-1 Exponents
Additional Example 4 Continued
A 7-sided figure has 14 diagonals. You can
verify your answer by sketching the diagonals.
Course 3
4-1 Exponents
Check It Out: Example 4
1
Use the formula 2 (n2 – 3n) to find the number
of diagonals in a 4-sided figure.
1
2
1
2
1
2
1
2
1
2
(n2 – 3n)
(42 – 3 • 4) Substitute the number of sides for n.
(16 – 3 • 4) Evaluate the exponents.
(16 – 12)
Multiply inside the parentheses.
(4)
Subtract inside the parentheses.
2 diagonals
Course 3
Multiply
4-1 Exponents
Check It Out: Example 4 Continued
A 4-sided figure has 2 diagonals. You can verify
your answer by sketching the diagonals.
Course 3
4-1 Exponents
Lesson Quiz: Part I
Write in exponential form.
1. n • n • n • n
n4
2. (–8) • (–8) • (–8) • (h)
(–8)3h
3. Evaluate (–4)4
256
4. Evaluate x
–213
Course 3
•
z – yx for x = 5, y = 3, and z = 6.
4-1 Exponents
Lesson Quiz: Part II
5. A population of bacteria doubles in size every
minute. The number of bacteria after 5 minutes
is 15  25. How many are there after 5 minutes?
480
Course 3