Exponent Laws!
Write each expression as a product and then evaluate the following:
1)
32 x 32
2)
3)
22 x 25 Do you notice anything???
(­5)2 x (­5)4
Exponent Law for a Product of Powers
To multiply powers with the same base, add the exponents.
m
n
m+n
a x a = a
**must be the same base
The variable "a" is any interger, except 0.
The variable "m" and "n" are any whole numbers.
Write each of the following as a single power, then evaluate.
1) 72 x 74 2) (­2)5 x (­2)3
3) 45 x 4
What happens if we DIVIDE powers with the same base?
2)
1)
3)
SUBTRACTION!
Exponent Law for a Quotient of Powers
To divide powers with the same base, subtract the exponents.
m
n
a ÷ a = a
m­n
Where
m≥n
ex.
must be the same base
The variable "a" is any interger, except 0.
The variable "m" and "n" are any whole numbers.
Evaluate each of the folowing:
1) 310 ÷ 36 + 32
2) BEDMAS
Choice Work
Choose 3 parts from each question:
#4
#5
#6
#8
#10
You have 20 minutes to complete!
Evaluate
1)
2)
3)
Assessment Focus (Good Test Question, Folks!)
See page 77, Question #12
An alfalfa field is a rectangle 104m long and 103m wide.
Fill in the following chart
(23)4
= 23 x 23 x 23 x 23 From section 2.4
= 23+3+3+3
= 212 3 4
How is this related to ? (2 )
Exponent Law for a Power of a Power
To raise a power to a power, multiply the exponents.
m n
mn
(a ) = a
The variable "a" is any integer, except 0.
The variable "m" and "n" are any whole numbers.
Try this
Express the following as a single power
1) (57)8
2) (102)3
3) [(­2)4]3
2) (52)3
3) [(­3)2]4
Evaluate
1) (23)2
Fill in the following chart
Exponent Law for a Power of a Product
m
m m
(ab) = a b
The variables "a" and "b" are any integer, except 0.
The variable "m" is any whole numbers.
Try this
Write as a power
1) [(­5)3]7
2) ­(35)4
3) (48)2
Let's Investigate
Step 1) Write the above as a repeated multiplication.
Step 2) Look at the numerators can you express that as a single power
Step 3) Look at the denominators can you express that as a single power
What did you discover?
Exponent Law for a Power of a Product
BUT b≠0
The variables "a" and "b" are any integer, except 0.
The variable "m" is any whole numbers.