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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
4-1 Exponents
Learn to evaluate expressions with
exponents.
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
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 “ negative 6 to the 3rd
power” or “negative 6 cubed”.
4-1 Exponents
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
Identify how many
times d is a factor.
4-1 Exponents
Example 1 (Cont...)
Write in exponential form.
C. 7 • 7 • b • b
2
7•7•b•b=7b
2
Identify how many
times 7 and b are
used as a factor.
4-1 Exponents
Example 2: Simplifying Powers
Simplify.
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.
4-1 Exponents
Example 2: Simplifying Powers
Simplify.
C. (–4)4
(–4)4= (–4) • (–4) • (–4) • (–4)
= 256
D.
Find the product
of four –4’s.
Find the product of eight 1/2’s.
4-1 Exponents
Example 3
Simplify.
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
4-1 Exponents
Example 3
Simplify.
C. –(5)2
–(5)2 = –(5) • (5)
= –25
Find the product of
two 5’s and then
make the answer
negative.
D. 97
Find the product of
97 = 9 • 9 • 9 • 9 • 9 • 9 • 9
= 4,782,969
seven 9’s.
4-1 Exponents
Example 4: 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.
4-1 Exponents
Example 5
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.
4-1 Exponents
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems
4-1 Exponents
Lesson Quiz: Part I
Write in exponential form.
1. n• n
•
2. (–8)
•
n4
n• n
(–8)
•
(–8)
3. Evaluate (–4)4
4. Evaluate x
–213
•
•
(h)
(–8)3h
256
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
4-1 Exponents
Lesson Quiz for Student Response Systems
1. Write g• g • g
A. 5g
B. g + 5
C. g5
D. g5
•
g
•
g in exponential form.
4-1 Exponents
Lesson Quiz for Student Response Systems
2. Evaluate (–3)4.
A. 12
B. –12
C. 81
D. –81
4-1 Exponents
Lesson Quiz for Student Response Systems
3. Evaluate gh + 3k – gk for g = 2, h = 4, and k = 3.
A. 6
B. 7
C. 9
D. 11