Objectives You will be able to: 1. Multiply monomials. 2.Simplify expressions with monomials. 3.Divide Monomials 4.Simplify negative exponents. A monomial is a 1. number, 2. variable, or 3. a product of one or more numbers and variables. Examples: 5 y 3x2y3 Why are the following not
monomials? x+y addition x y division 2 - 3a subtraction Multiplying Monomials When multiplying monomials, you ADD the exponents. 1) x2 x4 x2+4 x6 2) 2a2y3 3a3y4 6a5y7 Simplify m3(m4)(m)
1. 2. 3. 4. m7 m8 m12 m13 Power of a Power When you have an exponent with an exponent, you multiply those exponents. 1) (x2)3 x2 3 x6 2) (y3)4 y12 Simplify (p2)4
1. 2. 3. 4. p2 p4 p8 p16 Power of a Product When 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
Simplify (4r)3 1. 2. 3. 4. 12r3 12r4 64r3 64r4 Power of a Monomial This is a combination of all of the other rules. 1) (x3y2)4 x3 4 y2 4 x12 y8 2) (4x4y3)3 64x12y9
Simplify (3a2b3)4 1. 2. 3. 4. 12a8b12 81a6b7 81a16b81 81a8b12 Dividing Monomials When dividing monomials, subtract the exponents. 5 b bbbbb 5-2
3 1. 2 = b = b b bb 7 5 m n 7-1 5-2 = m6 n3 2. = m n 2
mn 3 7 xy 3. 2 6 x y 3 7 x y 3 2 7 6 = xy x y 2 6 x y
8 3 81a b 4. 5 9a b 8 3 81a b 8-5 3-1 3 2 9a b = 9a b 5 9a b 2
7 64g h Simplify 5 16gh 1. 2. 3. 4. 48g2h2 48gh2 4g2h2 4gh2 Heres a tricky one! 3 3
3m n 5. 3 2 3m n = 1m n = n 0 What happened to the m? 3 3 3m n 3mmmn n n 3 2 3m n 3mmmn n
3 They canceled out! m 1 3 m There are no ms 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! 3 1 3 0
3 1 x 1 x 0 x 1 m3 1 3 m 0 m 1 Negative Exponents A negative exponent means you move the
base to the other side of the fraction and make the exponent positive. -n n a 1 1 a n a n or -n = a 1 a a 1 -n Notice that the base with the negative exponent moved and became positive! Simplify.
6. x y -4 0 You can not have negative or zero exponents in your answer. 1 -4 0 x 4 and y 1 x 1 1 1 4 4
x x Simplify 1. p2 2. p12 1 3. p2 4. 1 . p12 . -7 p -5 p
4 2 Simplify. 3r s 1 4 3 2 4 1 2 r s rs 2 7. 3 4 r 6 6 6s 18r s You cant leave the negative exponent! There is another way of doing this without negative exponents.
If you dont want to see it, skip the next slide!!! Simplify (alternate version). 4 2 3r s 7. 3 4 18r s 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. 4 2
4-3 r 3r s 1r 2 3 4 4-2 6s 18r s 6s Notice that you did not have to work with negative exponents! This method is quicker! Simplify. 3
x 8. 4 x Get rid of the negative exponent. 3 x 1 1 4 3 4 7 x xx x 5 2
Simplify. r s Get rid of the negative exponents. 9. 3 3 rs 5 2 3 r s s s 3 3 5 3 2 8 rs rrs r
Simplify. 2 2 3 x y Get rid of the parentheses. 10. 4x 6 4 x y x y 3 6 4 x 4x 2 3
3 2 2 Get rid of the negative exponents. 2 3 6 4 4 4 y x y y 3 6 3 6 6
12 4 x 4x x 64x 1 2 -3x y Simplify 2xy 2 3 3 1. 2. 3. 4. .
. . 9x 8y11 -9x 8y11 -9x 8y 7 9x 8y 7 . Homework Page 226: 18-42 even