Download Document

Warm-ups
Solve:
1.) 2
3.) 4
5
4
=
=
=
=
=
=
=
=
=
2•2•2•2•2
4•2•2•2
8•2•2
16•2
32
4•4•4•4
16•4•4
64•4
256
2.) 3
3
= 3•3•3
= 9•3
= 27
4.) (3•4•60)
0
= 1
Anything to the
0 power is 1
7.3-MULTIPLYING EXPONENTS
Exponent
What is an exponent?
3
4
= 3•3•3•3
Base
Base - Tells you what # you multiply.
Exponent - Tells you how many times you
multiply
What if we multiply two exponents with the
same base?
Exponent
3  3 = 3•3•3•3  3•3•3•3•3
4
5
3
Base
How many 3’s do we have now?
9
So the base is 3 and the exponent is 9.
3
9
9
3  3 = 3•3•3•3  3•3•3•3•3  3
44
99
55
What do you notice about the exponents?
What does
+
= ?
When multiplying exponents, we can:
1.) Keep the base number and
2.) Add the exponents.
Oh,
I see!
a a  a
m
n
a a  a
3
2
mn
5
Type 1:
Simplify:
4 4  4
8
4
3
3+5
5
 Keep the base
 Add the exponents
Type 2:
x x x
3
6
x
3+6
9
 Keep the base
 Add the exponents
You try:
Simplify:
7 7
6
4
7
7
z z  z
5
9
z
6+4
 Keep the base
 Add the exponents
10
5+9
14
 Keep the base
 Add the exponents
Type 3:
Simplify:
4 y  3 y = 4●3 y
2
4
2+4
 12 y
1.) Multiply the numbers in front.
2.) Keep the base number (or variable)
3.) Add the exponents.
6
You try:
Simplify:
2a  4a
5
= 2•4 a
3
5+3
= 8a
8
1.) Multiply the numbers in front.
2.) Keep the base number (or variable)
3.) Add the exponents.
Type 4:
Simplify:
5 xy  2 x y = 5●2 x y
1
3
3
6
 10 x y
1+3 3+6
4
1.) Multiply the numbers in front.
2.) Keep the common base number (or variable)
3.) Add the exponents.
4.) Keep the common base number (or variable)
5.) Add the exponents.
9
Try this:
Simplify: 4 x
4
y  4 x y = 4●4 x y
3
2
5
 16 x y
4+2 3+5
1.) Multiply the numbers in front.
2.) Keep the common base number (or variable)
3.) Add the exponents.
4.) Keep the common base number (or variable)
5.) Add the exponents.
6
8
2n  3n
5
2
 6n
 6n
5 ( 2)
3
C
-8
•C
-3
=C
= 1
3
C
5