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ObjectivesThe student will be able to:
1. multiply monomials.
2. simplify expressions with monomials.
A monomial is a1. number,
2. variable, or
3. a product of one or more numbers and variables.
Examples:
5
y
3x2y3
Multiplying MonomialsWhen multiplying monomials, you
ADD the exponents.
1) x2 • x4
x2+4
x6
2) 2a2y3 • 3a3y4
6a5y7
Power of a PowerWhen you have an exponent with an
exponent, you multiply those exponents.
1) (x2)3
x2• 3
x6
2) (y3)4
y12
Power of a ProductWhen you have a power outside of the
parentheses, everything in the parentheses is raised to that power.
1) (2a)3
23a3
8a3
2) (3x)2
9x2
Power of a MonomialThis is a combination of all of the other
rules.
1) (x3y2)4
x3• 4 y2• 4
x12 y8
2) (4x4y3)3
64x12y9
When dividing monomials, subtract the exponents.
1.
2.
Dividing Monomials
= m6 n3
5
2
b
b
7 5
2
m n
mn
= b5-2b b b b b
b b
= b3
= m7-1n5-2
5. 3m3n3
3m3n2 = 1m0n
Here’s a tricky one!
What happened to the m?
= n
3 3
3 2
3m n 3m m m n n n
3m n 3m m m n n
They canceled out!
There are no m’s left over!This leads us to our next rule…
3
31
m
m
Zero ExponentsAnything to the 0 power is equal to 1.
a0 = 1True or False?
Anything divided by itself equals one.True!
See for yourself!
3
3
3 x m1 1 1
3 x m
0 0 03 1 x 1 m 1
A negative exponent means you move the base to the other side of the fraction and make the exponent positive.
-n n-n n
n -n
a 1 1 aa or = a
1 a a 1
Negative Exponents
Notice that the base with the negative exponent moved and became positive!
Simplify.
-4 04
1x and y 1
x
6. x-4 y0
You can not have negative or zero exponents in your answer.
4 4
1 1
x
1
x
Simplify.
7. 3r4s2
18r3s44 3 2 41
r s6
21rs
6
2
r
6s
You can’t leave the negative exponent!
There is another way of doing this without negative exponents.
If you don’t want to see it, skip the next slide!!!
10. x 3y2 2
4x2 3
x 6y4
43 x6
4
12
y
64x
Get rid of the parentheses.
Simplify.
23 2
32
x y
4x
Get rid of the
negative exponents.
4
3 6 6
y
4 x x
x 6y4
43 x6
How wide is our universe?210,000,000,000,000,000,000,000 miles
(22 zeros)
This number is written in decimal notation. When numbers get this large,
it is easier to write them in scientific notation.
Scientific Notation
A number is expressed in scientific notation when it is in the form
a x 10n
where a is between 1 and 10
and n is an integer
Write the width of the universe in scientific notation.
210,000,000,000,000,000,000,000 miles
Where is the decimal point now?
After the last zero.
Where would you put the decimal to make this number be between 1 and 10?
Between the 2 and the 1
2.10,000,000,000,000,000,000,000.
How many decimal places did you move the decimal?
23When the original number is more than 1,
the exponent is positive.The answer in scientific notation is
2.1 x 1023
1) Express 0.0000000902 in scientific notation.
Where would the decimal go to make the number be between 1 and 10?
9.02The decimal was moved how many places?
8When the original number is less than 1, the
exponent is negative.9.02 x 10-8
Write 28750.9 in scientific notation.
1. 2.87509 x 10-5
2. 2.87509 x 10-4
3. 2.87509 x 104
4. 2.87509 x 105
2) Express 1.8 x 10-4 in decimal notation.0.00018
3) Express 4.58 x 106 in decimal notation.
4,580,000
Write (2.8 x 103)(5.1 x 10-7) in scientific notation.
1. 14.28 x 10-4
2. 1.428 x 10-3
3. 14.28 x 1010
4. 1.428 x 1011
Write in PROPER scientific notation.(Notice the number is not between 1 and 10)
4) 234.6 x 109
2.346 x 1011
5) 0.0642 x 104
6.42 x 10 2