8.3 multiplying exponents. 8.3 – multiplying exponents warm up write each expression using an...
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8.3
Multiplying Exponents
8.3 – Multiplying Exponents8.3 – Multiplying ExponentsWarm Up
Write each expression using an exponent.1. 2 • 2 • 2
2. x • x • x • x
3.
Write each expression without using an exponent.
4. 43
5. y2
6. m–4
23
4 • 4 • 4
y • y
8.3 – Multiplying Exponents8.3 – Multiplying Exponents
8.3 – Multiplying Exponents8.3 – Multiplying Exponents
Given Think of it like this:
x * x * x * x * x * x * xx * x * x * x * x * x * x
?43 xx
8.3 – Multiplying Exponents
In general REMEMBER – the basesbases MUSTMUST be the
same
baba xxx
Products of powers with the same base can be found by writing each power as a repeated multiplication.
Notice the relationship between the exponents in the factors and the exponents in the product 5 + 2 = 7.
8.3 – Multiplying Exponents8.3 – Multiplying Exponents
Simplify.
A.
Since the powers have the same base, keep the base and add the exponents.
B.
Group powers with the same base together.
Add the exponents of powers with the same base.
8.3 – Multiplying Exponents8.3 – Multiplying Exponents
Simplify.
C.
D.
1
Group powers with the same base together.
Add the exponents of powers with the same base.
Group the positive exponents and add since they have the same base
Add the like bases.
8.3 – Multiplying Exponents8.3 – Multiplying Exponents
A number or variable written without an exponent actually has an exponent of 1.
Remember!
10 = 101
y = y1
8.3 – Multiplying Exponents8.3 – Multiplying Exponents
a. Simplify.
Since the powers have the same base, keep the base and add the exponents.
b.
Group powers with the same base together.
Add the exponents of powers with the same base.
8.3 – Multiplying Exponents8.3 – Multiplying Exponents
Simplify.
c.
Group powers with the same base together.
Add.
8.3 – Multiplying Exponents8.3 – Multiplying Exponents
Simplify.
d.
Group the first two and second two terms.
Divide the first group and add the second group.
Multiply.
8.3 – Multiplying Exponents8.3 – Multiplying Exponents
8.3 – Multiplying Exponents
Examples:
a.
b.
c.
43 77
214 444
86 66
8.3 – Multiplying Exponents
Multiplying powers in algebraic expressionsMultiplying powers in algebraic expressionsWhen multiplying, only combine the
things that are similar.Example:
you can rewrite it as
or
43 52 xx 4352 xx
710x
8.3 – Multiplying Exponents
Try:
682 qq 435 936 xyx
8.4
More Multiplying Exponents
To find a power of a power, you can use the meaning of exponents.
Notice the relationship between the exponents in the original power and the exponent in the final power:
8.4 – More Multiplying Exponents8.4 – More Multiplying Exponents
8.4 – More Multiplying Exponents8.4 – More Multiplying Exponents
Simplify.
Use the Power of a Power Property.
Simplify.
1
Use the Power of a Power Property.
Zero multiplied by any number is zero
Any number raised to the zero power is 1.
8.4 – More Multiplying Exponents8.4 – More Multiplying Exponents
Simplify.
Use the Power of a Power Property.
Simplify the exponent of the first term.
Since the powers have the same base, add the exponents.
Write with a positive exponent.
C.
8.4 – More Multiplying Exponents8.4 – More Multiplying Exponents
Simplify.
Use the Power of a Power Property.
Simplify.
1
Use the Power of a Power Property.
Zero multiplied by any number is zero.
Any number raised to the zero power is 1.
8.4 – More Multiplying Exponents8.4 – More Multiplying Exponents
Simplify.
Use the Power of a Power Property.
Simplify the exponents of the two terms.
Since the powers have the same base, add the exponents.
c.
8.4 – More Multiplying Exponents8.4 – More Multiplying Exponents
Powers of products can be found by using the meaning of an exponent.
8.4 – More Multiplying Exponents8.4 – More Multiplying Exponents
Simplify.
Use the Power of a Product Property.
Simplify.
Use the Power of a Product Property.
Simplify.
A.
B.
8.4 – More Multiplying Exponents8.4 – More Multiplying Exponents
Simplify.
Use the Power of a Product Property.
Use the Power of a Product Property.
Simplify.
C.
8.4 – More Multiplying Exponents8.4 – More Multiplying Exponents
Simplify.
Use the Power of a Product Property.
Simplify.
Use the Power of a Product Property.
Use the Power of a Product Property.
Simplify.
8.4 – More Multiplying Exponents8.4 – More Multiplying Exponents
Simplify.
Use the Power of a Product Property.
Use the Power of a Product Property.
Combine like terms.
Write with a positive exponent.
c.
8.4 – More Multiplying Exponents8.4 – More Multiplying Exponents
Simplify.
1. 32• 34
3.
5.
7.
2.
4.
6.
(x3)2
8.4 – More Multiplying Exponents8.4 – More Multiplying Exponents
7. The islands of Samoa have an approximate area of 2.9 103 square kilometers. The area of Texas is about 2.3 102 times as great as that of the islands. What is the approximate area of Texas? Write your answer in scientific notation.
8.4 – More Multiplying Exponents8.4 – More Multiplying Exponents