Transcript Document 7452137

7.5 Properties of Exponents and
Scientific Notation
Exponents and Exponential
Expressions
• Exponents are used to write products of
repeated factors.
– Ex. 3 • 3 • 3 • 3 = 34
• In the above example, the 4 is the exponent
and 3 is the base.
• The quantity 34 is called an exponential
expression.
Evaluating Exponential Expressions
• Evaluate each exponential expression.
72
-42
(-2)4
 Evaluate each exponential
expressions.
51
53
-84
(-2)5
-24
The Product Rule
• Product Rule for Exponents:
am • an = am + n
• Apply the product rule for exponents in each
case.
34 • 37
(5y2)(-3y4)
Apply the product rule for
exponents in each case.
53 • 5
y3 • y8 • y2
(7p3q)(2p5q2)
The Power Rules
Power Rules for Exponents
a 
m n
a
mn
 ab 
m
m
a b
m m
a
a
   m
b
b
m
Applying the Power Rules
• Simplify each expression.
(p8)3
(3y)4
2
 
3
4
 Simplify each expression.
(6p7)2
 2m 


 z 
5
3
Zero and Negative Exponents
Zero Exponent
a0 = 1
Negative Exponent
1
n
a  n
a
Special Rules for Negative Exponents
1
n

a
an
n
m
a
b
 n
m
b
a
Evaluating Exponential Expressions
• Evaluate each expression.
120
5z-3
(-m)-4
(8k)0
3-1 + 4-1
1
2 3
-60
2-3
3
 
7
2
The Quotient Rule
Quotient Rule for Exponents
m
a
mn
a
n
a
Applying the Quotient Rule
• Simplify each quotient.
7
3
2
3
2
8
5
8
12
9
12
7
7
5
2
3
2
k
12
k
10
z
8
z
Writing Expressions with No
Negative Exponents
• Simplify each expression so that no negative
exponents appear in the final result.
32 • 3-5
(x-4)6
x 4 y 2
2 5
x y
Simplify each expression so that no
negative exponents appear in the final
result.
x-3 • x-4 • x2
(4-2)-5
(23x-2)-2
Scientific Notation
• Many of the numbers that occur in science are
very large or very small.
• Writing these numbers is simplified by using
scientific notation.
Scientific Notation
A number is written in scientific notation
when it is expressed in the form a x 10n,
where 1 ≤ |a|< 10 and n is an integer.
IB Exam Information
(NOT in your book!)
• Express your answer in the form a x 10k,
where 1 ≤ |a|< 10 and k Є .
• FYI:
Є means “is an element of”
represents “all integers”
Converting to Scientific Notation
• Convert each number from standard notation
to scientific notation.
8,200,000
.000072
Convert each number from standard
notation to scientific notation.
46,500
.0051
Converting from Scientific Notation
• Convert each number from scientific notation
to standard notation.
6.93 x 105
4.7 x 10-6
Convert each number from scientific
notation to standard notation.
2.317 x 105
1.63 x 10-4
Using Scientific Notation in
Computation
• Evaluate 1,920, 000  .0015 by using scientific
.000032  45, 000
notation.
Evaluate the following by using
scientific notation.
.018  20, 000
300  .0004