Objectives The student will be able to 1

Objectives The student will be able to: 1. multiply monomials. 2. simplify expressions with monomials. SOL: A. 2 a Designed by Skip Tyler, Varina High School

A monomial is a 1. number, 2. variable, or 3. a product of one or more numbers and variables. Examples: 5 y 3 x 2 y 3

Why are the following not monomials? x+y addition division 2 - 3 a subtraction

Multiplying Monomials When multiplying monomials, you ADD the exponents. 1) x 2 • x 4 x 2+4 x 6 2) 2 a 2 y 3 • 3 a 3 y 4 6 a 5 y 7

Simplify 1. 2. 3. 4. m 7 m 8 12 m 13 m 3 4 m (m )(m)

Power of a Power When you have an exponent with an exponent, you multiply those exponents. 1) (x 2)3 x 2 • 3 x 6 2) (y 3)4 y 12

Power of a Product When you have a power outside of the parentheses, everything in the parentheses is raised to that power. 1) (2 a)3 23 a 3 8 a 3 2) (3 x)2 9 x 2

Power of a Monomial This is a combination of all of the other rules. 1) (x 3 y 2)4 x 3 • 4 y 2 • 4 x 12 y 8 2) (4 x 4 y 3)3 64 x 12 y 9

Simplify 1. 2. 3. 4. p 2 p 4 8 p 16 p 2 4 (p )

Simplify 1. 2. 3. 4. 12 r 3 12 r 4 3 64 r 4 64 r 3 (4 r)

Simplify 1. 2. 3. 4. 12 a 8 b 12 81 a 6 b 7 16 81 81 a b 8 12 81 a b 2 3 4 (3 a b )

Dividing Monomials When dividing monomials, subtract the exponents. 1. 2. = 5 -2 b = 3 b = m 7 -1 n 5 -2 = m 6 n 3

= xy = 3 2 9 a b

Simplify 1. 2. 3. 4. 48 g 2 h 2 48 gh 2 4 g 2 h 2 4 gh 2

Here’s a tricky one! = 0 1 m n =n What happened to the m? 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. a 0 = 1 True or False? Anything divided by itself equals one. True! See for yourself!

Negative Exponents A negative exponent means you move the base to the other side of the fraction and make the exponent positive. Notice that the base with the negative exponent moved and became positive!

Simplify. 6. -4 0 x y You can not have negative or zero exponents in your answer.

Simplify 1. p 2 2. p 12 3. 4. . .

Simplify. 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!!!

Simplify (alternate version). Look and see (visualize) where you have the larger exponent and leave the variable in that location. Subtract the smaller exponent from the larger one. In this problem, r is larger in the numerator and s is larger in the denominator. Notice that you did not have to work with negative exponents! This method is quicker!

Simplify. Get rid of the negative exponent.

Simplify. Get rid of the negative exponents.

Simplify. Get rid of the parentheses. Get rid of the negative exponents.

Simplify 1. 2. 3. 4. . .

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