exponent rules – day 1 zero and negative exponents
TRANSCRIPT
Exponent Rules – Day 1
Zero and Negative Exponents
Zero Exponents
Anything with an exponent of zero reduces to 1.
Examples:
090)4( 0723,100,5
Negative Exponents
If an exponent is negative, you can make it positive by moving it.
If it is in the denominator, move it to the numerator.
If it is in the numerator, move it to the denominator.
Examples
2
9
4
2
1
7
5
4
x
w
Simplifying Exponents
Simplify each exponent
2
3
0
4
3
)4(
)7(
3
Simplifying Exponential Expressions
Simplify each expression
30
21
4
3
3
1
4
zxy
ba
w
yx
Evaluating an exponential expression
Do not forget to follow the order of operations (PEMDAS)
Evaluate if:
223
3,2
tm
tm
Examples
Evaluate the following expressions if n = -2 and
w = 5.
2
4
0
2
1
03
1
nw
n
w
w
n
wn
Quick Check: Make sure you understand!
Simplify each expression:
Evaluate for x = 3, y = -2
) )((zyxx
n -6404308
5
237
324 yx
Homework! Practice! Study!
Big Green pg. 397 (2 - 44 even)
Exponent Rules – Day 2
Scientific Notation
Scientific Notation Rules
In the form:
n is an integer
a is between 1 and 10
Examples:
na 10
10136 101.2 1043.5 104.3
Scientific Notation or not?
4
7
5
3
12
1052
1042.3
1011.6
1084.0
1029.56
Writing a number in Scientific Notation
If the number is very large (>1) the exponent will be positive
If the number is very small (<1) the exponent will be negative
Why?
Examples
56,900,000
0.00985
Examples
267,000
0.0000325
Writing a number in standard notation
11
6
102
1055.1
More examples
4
12
106.5
102.3
Ordering Numbers
Put the numbers in scientific notation
Order the powers of 10
Arrange decimals of the same power of 10 in order
Write the original numbers in order
Examples
greatest least to from 534 and ,1012.5 ,10052.0Order 57
Examples
greatest least to from
1061 and ,10067.0 ,1063 ,102.60Order 2345
Multiplying a number in scientific Notation
)102.1(5.0
)104(7
3
5
Examples
)102(4.0
)106(5.2
9
3
Homework! Practice! Study!
Big Green pg. 402-403
(2 - 40 even)
Exponent Rules: Day 3
Multiplication Properties of Exponents
Multiplying Powers with the same base
If the bases are the same, you can add the exponents.
Examples:
2242945 1
333h
hhh
More examples
623
34
63
34
777
22
55
)11(11
Multiplying Powers in an expression
nnn
aa
nn
xxx
7
32
32
5
25
42
More Complex Examples
mnm
yxy
aba
xyx
cdc
7
272
325
22
423
5
84
234
Multiplying Numbers in Scientific Notation
)106)(105.2(
)104)(107(
38
52
More Examples
)107)(109(
)103)(105.1(
96
42
Quick Check: Make sure you understand! Simplify:
)107)(103(
432
54
53
42542
04652
qpqaba
yxxppp
Homework! Practice! Study!
Big Green pg. 407 – 408
(8 - 26 even)
(32 - 50 even)
Exponent Rules: Day 4
Dealing with Powers of exponents
Raising a Power to a Power
When raising an exponent to an exponent, multiply the exponents together.
Example:
824 5)5(
More Examples
74
63
52
)(
)(
)(
a
x
n
More Complex Examples
5224
272
534
235
)()(
)(
)(
)(
aa
tt
nn
cc
Raising a product to a power
Apply the power rule (multiply the exponents) to each factor in the parentheses.
Example:
4444 813)3( xxx
Examples
40
25
4
42
)3(
)4(
)2(
)2(
t
g
z
x
More Complex Examples
4532
422
)3()(
)3)((
cc
xyx
More complex examples
233
3253
)5()6(
)3()2(
mmn
aba
Scientific Notation Examples
343
28
)102(10
)103(
More Scientific Notation Examples
322
282
)105(5
)103(10
Homework! Practice! Study!
Big Green pg. 413-414(2 - 30 even)
(42 – 50 even)
Exponent Rules: Day 5
Division Properties of Exponents
The Division Rule
When dividing exponents of the same base; subtract the exponents
Example:
43
7
33
3
Examples:
9
4
45
31
14
6
b
b
dc
dc
a
a
More Examples
nm
nm
ba
ba
z
z
3
21
34
2
5
10
More Examples
63
43
34
412
jp
jp
zxy
zyx
Scientific Notation Examples
4
12
8
3
8
7
105.2
105.7
108
102
10705.2
105.3
Raising a quotient to a power
Raise everything within the parenthesis to the power!
Example:
3
33
y
x
y
x
Examples
2
3
7
3
2
3
2
2
4
t
y
x
x
More Complex Examples
2
1
5
2
7
2
2
1
4
3
m
a
s
r
All Exponent Rules Combined!
3
024
353
0
93
42
)()2(
)2(4
xyz
yxx
xyzz
zyx
zxy
Homework! Practice! Study!
Big Green pg. 420-421
(10 - 18 even)
(30 - 48 even)
(52 - 58 even)