Post on 18-Jan-2018
description
Section 5.1a
Monomials
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Def: A monomial is an expression that is a number, a variable or the product of a number and one or more variables.
Constants are monomials with no variables
3,
Examples:
x3,5xyz
Coefficient
Exponent
Def: The degree of a monomial is the sum of the exponents of its variables.
Examples:
x2
y3z
2w5
4
2nd degree
4th degree(3 + 1 = 4)5th degree
0th degree
Rules of Exponents
1. a0 =
2. am•an =
3. a-n =
1
am+n Why ?
1/(an) Why ?
Why ? = a(1-1) = a0
a2•a3 = a•a•a•a•a
1a2
a(0 2) = a-2
= a5
1aa
a1
a1
Rules of Exponents
4.am÷an =
5.(am)n =
6. a(m/n) =
amn
a(m-n)
am•n
Why ?
Why ?
a3
a2a a aa a
= a1
(a4 )2 a4 a4 = a8
Why ? 2 626
aa
23336 )()()( aaaa 3a
1. 34 xx
Simplify
2. 2
8
dd
3. ))(( 53 yy
4. )4)(5( 32 xyyx
Add the exponents
Subtract the exponents
Add the exponents
Multiply the coeficientsAdd the exponents
1a 1
11a
Remember: division is multiplying by the reciprocal
If you have a negative exponent in a fraction “flip” it and make the exponent +
1a 1
a1
1
a 1
11a1
and
11 a 1a
Simplify
5.
24ab 2
6a 1b 3
6.
(312 )(32)
7.
(2n3)4
Homework
Page 259Problems: 19-45 (odd)