2-6 Exponents
Course 3
Warm Up
Problem of the Day
Lesson Presentation
Warm UpFind the product.
Course 3
2-6 Exponents
6251. 5 • 5 • 5 • 5
2. 3 • 3 • 3
3. (–7) • (–7) • (–7)
4. 9 • 9
27
–343
81
Problem of the Day
What two positive integers when multiplied together also equal the sum of the same two numbers?
Course 3
2-6 Exponents
2 and 2
Learn to evaluate expressions with exponents.
Course 3
2-6 Exponents
Course 3
2-6 Exponents
Vocabulary
power
exponential form
exponent
base
The term 27 is called a power. If a number is in exponential form, the exponent represents how many times the base is to be used as a factor.
Course 3
2-6 Exponents
7
ExponentBase
2
Course 3
2-6 Exponents
Identify how many times 4 is a factor.4 • 4 • 4 • 4 = 44
Write in exponential form.
Additional Example 1A & 1B: Writing Exponents
A. 4 • 4 • 4 • 4
Identify how many times d is a factor.
d • d • d • d • d = d5
B. d • d • d • d • d
Read 44 as “4 to the 4th power.”Reading Math
Course 3
2-6 Exponents
Identify how many times –6 is a factor.
(–6) • (–6) • (–6) = (–6)3
Identify how many times 5 is a factor.5 • 5 = 52
Additional Example 1C & 1D: Writing Exponents
C. (–6) • (–6) • (–6)
D. 5 • 5
Write in exponential form.
Course 3
2-6 Exponents
Identify how many times x is a factor.x • x • x • x • x = x5
Write in exponential form.
Try This: Example 1A & 1B
A. x • x • x • x • x
Identify how many times d is a factor.
d • d • d = d3
B. d • d • d
Course 3
2-6 Exponents
Identify how many times –3 is a factor.
(–3) • (–3) • (–3) • (–3) = (–3)4
Identify how many times 7 is a factor.7 • 7 = 72
Try This: Example 1C & 1D
C. (–3) • (–3) • (–3) • (–3)
D. 7 • 7
Write in exponential form.
Course 3
2-6 Exponents
A. 35
= 243
35 = 3 • 3 • 3 • 3 • 3Find the product of five 3’s.
= –243
= (–3) • (–3) • (–3) • (–3) • (–3)(–3)5
Find the product of five –3’s.B. (–3)5
Always use parentheses to raise a negative number to a power.
Helpful Hint
Evaluate.
Additional Example 2A & 2B: Evaluating Powers
Course 3
2-6 Exponents
D. 28
= 256
28 = 2 • 2 • 2 • 2 • 2 • 2 • 2 • 2
= 256
= (–4) • (–4) • (–4) • (–4)(–4)4
C. (–4)4
Evaluate.
Additional Example 2C & 2D: Evaluating Powers Continued
Find the product of four –4’s.
Find the product of eight 2’s.
Course 3
2-6 Exponents
A. 74
= 240174 = 7 • 7 • 7 • 7
Find the product of four 7’s.
= –729= (–9) • (–9) • (–9)(–9)3
Find the product of three –9’s.B. (–9)3
Evaluate.
Try This: Example 2A & 2B
Course 3
2-6 Exponents
D. 97
= 25
97 = 9 • 9 • 9 • 9 • 9 • 9 • 9
= 4,782,969
= (–5) • (–5)(–5)2
C. (–5)2
Evaluate.
Try This: Example 2C & 2D
Find the product of two –5’s.
Find the product of seven 9’s.
Additional Example 3: Simplifying Expressions Containing Powers
Course 3
2-6 Exponents
= 47
Simplify (25 – 32) + 6(4).
= (32 – 9) + 6(4)
= (23) + 6(4)
= 23 + 24
Evaluate the exponents.
Subtract inside the parentheses.
Multiply from left to right.
Add from left to right.
Course 3
2-6 Exponents
Try This: Example 3
= –49
Simplify (32 – 82) + 2 • 3.
= (9 – 64) + 2 • 3
= (–55) + 2 • 3
= –55 + 6
Evaluate the exponents.
Subtract inside the parentheses.
Multiply from left to right.
Add from left to right.
(72 – 3 • 7)1
2
Additional Example 4: Geometry Application
Course 3
2-6 Exponents
Evaluate the exponent.
Multiply inside the parentheses.
Multiply
Substitute the number of sides for n.
Subtract inside the parentheses.
14 diagonals
(49 – 21)1
2
(n2 – 3n)1
2
(49 – 3 • 7)1
2
(28)1
2
Use the formula (n2 – 3n) to find the number of diagonals in a 7-sided figure.
1 2
Course 3
2-6 Exponents
Verify your answer by sketching the diagonals.
14 Diagonals
Additional Example 4 Continued
(42 – 3 • 4)1
2
Try This: Example 4
Course 3
2-6 Exponents
Evaluate the exponents.
Multiply inside the parentheses.
Multiply
Substitute the number of sides for n.
Subtract inside the parentheses.
2 diagonals
(16 – 12)1
2
(n2 – 3n)1
2
(16 – 3 • 4)1
2
(4)1
2
Use the formula (n2 – 3n) to find the number of diagonals in a 4-sided figure.
1 2
Course 3
2-6 Exponents
Verify your answer by sketching the diagonals.
2 diagonals
Try This: Example 4 Continued
Course 3
2-6 Exponents
Lesson Quiz: Part 1
Write in exponential form.
1. n • n • n • n
2. (–8) • (–8) • (–8)
256
3
(–8)3
3. Evaluate (–4)4
4. Simplify 99 – 3(4 • 23).
4n
Course 3
2-6 Exponents
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?
Lesson Quiz: Part 2
480
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