Transcript Exponent Laws I

Exponent Laws
Part I
Topic 2.4
Exponent Law for a Product of Powers
2 2 
3
5
What does
product mean?
5 5 
2
3
4 4 
4
6
How could you
solve this question?
What do you notice about the bases?
What happens to the exponents?
Will it work if the bases are not the same?
Law 1
• To multiply powers with the same base,
simply leave the base the same and add the
exponents.
• na x nb = na+b
The “Law”
• To multiply powers with the same base,
simply leave the base the same and add
the exponents.
EXAMPLES
6 6 
5 4
6
9
6
5
4
(2)  (2) 
4
7
 (2)
 (2)
4 7
11
Why does this work?
65
64
65 x 64 =
= (6 x 6 x 6 x 6 x 6) x (6 x 6 x 6 x 6)
=6x6x6x6x6x6x6x6x6
= 69 = 65+4
= 10077696
What do you think happens here?
(3)  (4) 
3
2
Follow
BEDMAS!
(2)  (2) 
3
2
The rule does NOT apply to ADDITION of same
base questions.
The rule does NOT apply to UNLIKE base
multiplication questions.
Exponent Law for a Quotient of Powers
2 2 
8
4
(5)

3
 5
5
4 4 
9
What does
quotient
mean?
How could you
solve this question?
6
What do you notice about the bases?
What happens to the exponents?
Will it work if the bases are not the same?
Law 2
• To divide powers with the same base simply
leave the base the same and subtract the
exponents.
•
na ÷
nb
=
na-b
a
n
a b
n
b
n
The “Law”
• To DIVIDE powers with the SAME base,
SUBTRACT the exponents.
EXAMPLES
(5)  (5) 
4
1
9
(7 )

5
7 
 (2)  (2) 
12
8
You might find it easier to write division questions in ‘fraction form’!
Why does this work?
777777777
7

5
77777
7
7  7  7  7  7 7777

77777
9
1 7  7  7  7
4
9 5
 7  7  2401

1
What do you think happens here?
3
6

2
3
(2)  (2) 
4
2
Follow
BEDMAS!
Law does NOT apply to SUBTRACTION of same
base questions.
Law does NOT apply to UNLIKE base DIVISION
questions.
Let’s try a few…
Write as a power.
4
(3)(3)

2
(3)
(2) (2) (2) 
3
3
5
Evaluate.
6  6 6 
2
3

2

(10) (10)  (10)  10 
4
6
4
7
ASSIGNMENT
PAGE 76
Discuss: #1, 2, 3
Complete:
4aceg, 5bdfh, 6, 8, 9, 10aceghij, 12abd,
13aceg, 17
Extension: 20, 21a, 22a