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4-1 Exponents
Warm UpWarm Up
Lesson PresentationLesson Presentation
Problem of the DayProblem of the Day
Lesson QuizzesLesson Quizzes
4-1 Exponents
Warm UpFind the product.
6251. 5 • 5 • 5 • 5
2. 3 • 3 • 3
3. (–7) • (–7) • (–7)
4. 9 • 9
27
–343
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
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.
Additional 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.
Additional 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
Identify how many times x is a factor.x • x • x • x • x = x5
Write in exponential form.
Check It Out: Example 1
A. x • x • x • x • x
Identify how many times d is a factor.
d • d • d = d3
B. d • d • d
4-1 Exponents
Identify how many times 7 and b are used as a factor.
7 • 7 • b • b = 72b2
Check It Out: Example 1
C. 7 • 7 • b • b
Write in exponential form.
4-1 Exponents
A. 35
= 243
35 = 3 • 3 • 3 • 3 • 3
Find 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
Simplify.Additional Example 2: Simplifying Powers
4-1 Exponents
D.
= 256
= (–4) • (–4) • (–4) • (–4) (–4)4
C. (–4)4
Simplify.
Additional Example 2: Simplifying Powers
Find the product of four –4’s.
Find the product of eight 1/2’s.
4-1 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
Simplify.
Check It Out: Example 2
4-1 Exponents
D. 97
= –25
97 = 9 • 9 • 9 • 9 • 9 • 9 • 9
= 4,782,969
= –(5) • (5) –(5)2
C. –(5)2
Simplify.
Check It Out: Example 2
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
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
Check It Out: Example 3
60 – 7(7)
Substitute 5 for x, 2 for y, and 60 for z.
Evaluate the exponent.
Subtract inside the parentheses.
Multiply from left to right.
60 – 7(25 – 52)
60 – 7(32 – 25)
60 – 49
Evaluate z – 7(2x – xy) for x = 5, y = 2, and z = 60.
z – 7(2x – xy)
Subtract. 11
4-1 Exponents
(72 – 3 • 7)1
2
Additional Example 4: Geometry Application
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 expression (n2 – 3n) to find the number of diagonals in a 7-sided figure.
1 2
4-1 Exponents
A 7-sided figure has 14 diagonals. You can verify your answer by sketching the diagonals.
Additional Example 4 Continued
4-1 Exponents
(42 – 3 • 4)1
2
Check It Out: Example 4
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
4-1 Exponents
A 4-sided figure has 2 diagonals. You can verify your answer by sketching the diagonals.
Check It Out: Example 4 Continued
4-1 Exponents
Lesson Quiz: Part I
Write in exponential form.
1. n• n • n• n
2. (–8) • (–8) • (–8) • (h)
256
–213
(–8)3h
3. Evaluate (–4)4
4. Evaluate x • z – yx for x = 5, y = 3, and z = 6.
4n
4-1 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 II
480
4-1 Exponents
1. Write g• g • g• g• g in exponential form.
A. 5g
B. g + 5
C. g5
D. g5
Lesson Quiz for Student Response Systems