Transcript Section 5.1

5.1
Exponents and Scientific Notation
1. Evaluate exponential forms with integer exponents.
2. Write scientific notation in standard form.
3. Write standard form numbers in scientific notation.
Objective 1
Evaluate exponential forms with
integer exponents.
Identify the base, exponent and evaluate.
2
Base:
5
 2
3
-2
Base:
2
Exponent: 5
Exponent:
3
32
Value:
Value: -8
When an equation in one variable is solved the answer is a point on a line.
 2
4
Base:
-2
Exponent:
Value:
16
2
Base:
4
4
2
Exponent: 4
Value:
-16
2
Evaluate: – 3
a) 9
b) –6
c) 6
d) 9
2
Evaluate: – 3
a) 9
b) –6
c) 6
d) 9
Evaluate:


2
 35  2 3  4
a) -93
b) 15
c) 105
d) None of the above

Evaluate:


2
 35  2 3  4
a) -93
b) 15
c) 105
d) None of the above

Evaluating Exponential Forms with Negative Bases
(negative number)even exponent = positive
(negative number)odd exponent = negative
Evaluate.
3
2
2
8
 
3
9


When
 an equation in one variable
 is apoint on a line

125 is solved the answer
 5
25
 5
.
Raising a Quotient to a Power
If a and b are real numbers, where b  0 and n is a
natural number, then
n
n
a
a
 
   n.
b b
Observe the pattern….
4
3  81
3
3  27
2
3 9
1
3 3
0
3  1
Zero as an Exponent
If a is a real number and a  0, then a 0  1.
Evaluate:
5
 5
0
0
1
1
When an equation in one variable is solved the answer is a point on a line.
0
5
–1
1
 
 25 
0
1
Evaluate:
6y
6y 0
0
6
1
When an equation in one variable is solved the answer is a point on a line.
 70
0
3 4
0
–1
1–1=0
Evaluate:
8w 
0
 6x  2y
2
0
-6x2
When an equation in one variable is solved the answer is a point on a line.
3  3
0
Indeterminate
Observe the pattern….
4
3  81
3
1
3
3  27
2
3 9
3
1
3 3
0
3 1
3
2
3
1
1
  1
3 3
1
1
  2
9 3
1
1

 3
27 3
Negative exponents are POSITIONAL only!!!
If a is a real number, where a  0 and n is a natural
number, then a
n
1
 n.
a
Exponents must be positive before you can evaluate!!!
Simplify:
2
3
1
1
 3 
8
2
3x
2

3
x2
When an equation in one variable is solved the answer is a point on a line.
 4x
3

4
x
3
 5x
3
 5x
3
5
x
3
 5  x 3  5 
1
x
3
x3
 5
1
 5x
3
Negative exponents are POSITIONAL only!!!
If a is a real number, where a  0 and n is a
natural number, then
1
n

a
.
n
a
Simplify:
3
2a
2
b

a 2b4
2
3 2
a b
c
3

b4 c 3
a2
When an equation in one variable is solved the answer is a point on a line.
3 2 3
3 x y

3 2
3 x
y
3
4h
5
2
m k

4m 2
h 5k
3
 
x
2

1
3
 
x
2
3
1 
x
2
1
9
x2
x
x
x

 1

 
9
9
3
2
2
2
If a and b are real numbers, where a  0 and b  0
n
n
a
b


and n is a natural number, then      .
b
a
–6
Evaluate: – 2
a)
b)
1

64
1
64
c) 12
d) 64
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–6
Evaluate: – 2
a)
b)
1

64
1
64
c) 12
d) 64
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Slide 5- 25
Objective 2
Write scientific notation in standard
form.
Scientific notation: A number expressed in the
n
a
10
, where a is a decimal number with
form
1  a  10 and n is an integer.
 3.45  105
2.45  10
3
Write 875,000 in scientific notation.
8.75  10
5
Write 0.0000000472 in scientific notation.
8
4.72  10
Write in standard form:
4.26 105
= 426,000
Write in standard form:
3.87 104
= .000387
Write 13,030,000 in scientific
notation.
a) 1303 104
b) 13.03 10
6
c) 1.303 107
d) 0.1303 109
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Copyright © 2011 Pearson Education, Inc.
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Write 13,030,000 in scientific
notation.
a) 1303 104
b) 13.03 10
6
c) 1.303 107
d) 0.1303 109
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Copyright © 2011 Pearson Education, Inc.
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6
Write 4.69 10 in standard notation.
a) 4,690,000
b) 4,690,000,000
c) 0.000000469
d) 0.00000469
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6
Write 4.69 10 in standard notation.
a) 4,690,000
b) 4,690,000,000
c) 0.000000469
d) 0.00000469
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