ObjectivesThe student will be able to:
1. multiply monomials.
2. simplify expressions with monomials.
SOL: A.2a
Designed by Skip Tyler, Varina High School
A monomial is a
1.number,
2.variable, or
3.a product of one or morenumbers and variables.
Examples:
5
y
3x2y3
Why are the following notmonomials? x + y
addition
division
2 - 3a
subtraction
Multiplying Monomials
When multiplying monomials, youADD the exponents.
1) x2 • x4
x2+4
x6
2) 2a2y3 • 3a3y4
6a5y7
Simplify m3(m4)(m)
1.m7
2.m8
3.m12
4.m13
Power of a Power
When you have an exponent with anexponent, you multiply those exponents.
1) (x2)3
x2• 3
x6
2) (y3)4
y12
Power of a Product
When you have a power outside of theparentheses, everything in theparentheses is raised to that power.
1) (2a)3
23a3
8a3
2) (3x)2
9x2
Power of a Monomial
This is a combination of all of the otherrules.
1) (x3y2)4
x3• 4 y2• 4
x12 y8
2) (4x4y3)3
64x12y9
Simplify (p2)4
1.p2
2.p4
3.p8
4.p16
Simplify (4r)3
1.12r3
2.12r4
3.64r3
4.64r4
Simplify (3a2b3)4
1.12a8b12
2.81a6b7
3.81a16b81
4.81a8b12
When dividing monomials, subtract theexponents.
1.
2.
Dividing Monomials
= m6 n3
= b5-2
= b3
= m7-1n5-2
= xy
= 9a3b2
Simplify
1.48g2h2
2.48gh2
3.4g2h2
4.4gh2
= 1m0n
Here’s a tricky one!
What happened to the m?
= n
They canceled out!
There are no m’s left over!
This leads us to our next rule…
Zero Exponents
Anything to the 0 power is equal to 1.
a0 = 1
True or False?Anything divided by itself equals one.
True!
See for yourself!
A negative exponent means you move thebase to the other side of the fraction andmake the exponent positive.
Negative Exponents
Notice that the base with the negativeexponent moved and became positive!
Simplify.
6.x-4 y0You can not have negative or zeroexponents in your answer.
1.p2
2.p12
3. .
4. .
Simplify
Simplify.
You can’t leave thenegative exponent!
There is another way of doing this withoutnegative exponents.
If you don’t want to see it, skip the nextslide!!!
Simplify (alternate version).
Look and see (visualize) where you havethe larger exponent and leave thevariable in that location. Subtract thesmaller exponent from the larger one.
In this problem, r is larger in the numerator and s islarger in the denominator.
Notice that you did not have to work with negativeexponents! This method is quicker!
Simplify.
Get rid of the negative exponent.
Get rid of the negative exponents.
Simplify.
Get rid of the parentheses.
Simplify.
Get rid of thenegative exponents.
1. .
2. .
3. .
4. .
Simplify
•Classwork
•Homework: