Download December 9, 2015 Section 4.1

4-1 Exponents
Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
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
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
4-1 Exponents
Learn to evaluate expressions with
exponents.
4-1 Exponents
Vocabulary
exponential form
exponent
base
power
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
Additional Example 1: Writing Exponents
Write in exponential form.
C. 5 • 5 • d • d • d • d
5 • 5 • d • d • d • d = 52d4
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
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
7•7•b•b=7b
2
Identify how many
times 7 and b are
used as a factor.
4-1 Exponents
Additional Example 2: Simplifying Powers
Simplify.
Find the product of five 3’s.
A. 35
35 = 3 • 3 •
3 = 243
•
5
B. (–3)
Find the product of five –3’s.
3•3
(–3)5 = (–3) • (–3) • (–3) • (–3) • (–3)
= –243
Helpful Hint
Always use parentheses to raise a negative number
to a power.
4-1 Exponents
Additional 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
Check It Out: Example 2
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
Check It Out: Example 2
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
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.
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.
4-1 Exponents
Additional Example 4: Geometry Application
1
Use the expression 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
Multiply
4-1 Exponents
Additional Example 4 Continued
A 7-sided figure has 14 diagonals. You can
verify your answer by sketching the diagonals.
4-1 Exponents
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems
4-1 Exponents
Warm-up: Page 159 # 1-10 all
Homework: Page 164 # 1-30 all
*no calculator on warm-up or homework*
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
Example 5
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
Multiply.
4-1 Exponents
A 4-sided figure has 2 diagonals. You can verify
your answer by sketching the diagonals.
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
A. 5g
B. g + 5
C. g5
D. g5
•
g•
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