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4-1 Exponents
Evaluating Algebraic Expressions
Exponential
Notation
4-1 Exponents
Exponent
Essential
Evaluating Algebraic Expressions
Question:
How do we write numbers
using exponents?
4-1 Exponents
Vocabulary
Evaluating
Algebraic Expressions
exponential form
exponent
base
power
4-1 Exponents
If a number is in exponential form, the
exponent
represents
how many
times the
Evaluating
Algebraic
Expressions
base is to be used as a factor. A number
produced by raising a base to an exponent
is called a power. 27 and 33 are
equivalent.
Exponent
Base
2
7
4-1 Exponents
Additional Example 1: Writing Exponents
Write
in exponential
form. Expressions
Evaluating
Algebraic
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) =
Reading Math
(–6)3
Identify how many
times –6 is a factor.
Read (–6)3 as “–6 to the 3rd power" or "–6
cubed”.
4-1 Exponents
Additional Example 1: Writing Exponents
Evaluating
Algebraic
Write
in exponential
form. Expressions
C. 5 • 5 • d • d • d • d
5 • 5 • d • d • d • d = 52d4
Identify how
many times 5
and d are each
used as a
factor.
4-1 Exponents
Check It Out! Example 1
Evaluating
Algebraic
Write
in exponential
form. Expressions
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
Evaluating
Algebraic
Write
in exponential
form. Expressions
C. 7 • 7 • b • b
2
2
7•7•b•b=7b
Identify how many
times 7 and b are
each used as a
factor.
4-1 Exponents
Additional Example 2: Simplifying Powers
Simplify.
Evaluating Algebraic Expressions
A. 35
35 = 3 • 3 • 3 • 3 • 3
Find the product.
= 243
B.
Find the product.
1
=
27
4-1 Exponents
Additional Example 2: Simplifying Powers
Evaluating Algebraic Expressions
Simplify.
C. (–4)4
(–4)4= (–4) • (–4) • (–4) • (–4)
Find the product.
= 256
D. –28
–28 = –(2 • 2 • 2 • 2 • 2 • 2 • 2 • 2) Find the product.
Then make the
= –256
answer negative.
4-1 Exponents
Evaluating Algebraic Expressions
Caution!
The expression (–4)4 is not the same as the
expression –44. Think of –44 as –1 ● 44.
By the order of operations, you must evaluate
the exponent before multiplying by –1.
4-1 Exponents
Check It Out! Example 2
Simplify.
Evaluating Algebraic Expressions
A. 74
74 = 7 • 7 • 7 • 7
= 2401
Find the product.
B.
Find the product.
1
=
8
4-1 Exponents
Check It Out! Example 2
Evaluate.
Evaluating Algebraic Expressions
C. (–5)2
(–5)2 = (–5) • (–5)
Find the product.
= 25
D. –94
–94 = –(9 • 9 • 9 • 9)
= –6,561
Find the product.
Then make the
answer negative.
4-1 Exponents
Evaluating Algebraic
Expressions
Exponent
Essential
Question:
How do we use exponents
within the order of
operations?
4-1 Exponents
In the Order of Operations
Evaluating Algebraic Expressions
The order in which mathematicians
perform math problems.
a)Parenthesis – working inward
outward
b)Exponents
c)Multiply or Divide – Left to Right
d)Add or Subtract – Left to Right
4-1 Exponents
Mnemonic
Evaluating Algebraic Expressions
•Please
•Parenthesis
•Excuse
•Exponents
•My Dear
•Multiply or Divide – Left to
Right
•Aunt Sally
•Add or Subtract – Left to Right
4-1 Exponents
4 X 6 – (3 + 4) + 22
Evaluating Parenthesis
Algebraic Expressions
4 x 6 - 7 + 22
Exponents
4X6–7+4
Multiply
24 – 7 + 4
Add or Subtract – Left to Right
17 + 4
21
4-1 Exponents
Additional Example 3: Using the Order of
Operations
y) + xy for x Expressions
Evaluate
x(yx – zAlgebraic
= 4, y = 2,
Evaluating
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
Simplify the powers.
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,
Evaluating Algebraic Expressions
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) Simplify the powers.
60 – 7(7)
Subtract inside the parentheses.
60 – 49
Multiply from left to right.
11
Subtract.
4-1 Exponents
Check It Out! Example 4
1
Use the expression 2 (n2 – 3n) to find the
Evaluating Algebraic Expressions
number of diagonals in a 4-sided figure.
1
2
1
2
1
2
1
2
(n2 – 3n)
(42 – 3 • 4) Substitute the number of sides for n.
(16 – 12)
Simplify inside the parentheses.
(4)
Subtract inside the parentheses.
2 diagonals
Multiply