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Def: The degree of a monomial is the sum of the exponents of its variables. Examples: x2x2 y3zy3z 2w 5 4 2nd degree 4th degree (3 + 1 = 4) 5th degree 0th degree

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Page 1: Section 5.1a Monomials. Def: A monomial is an expression that is a number, a variable or the product of a number and one or more variables. Constants

Section 5.1a

Monomials

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

Page 2: Section 5.1a Monomials. Def: A monomial is an expression that is a number, a variable or the product of a number and one or more variables. Constants

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

Page 3: Section 5.1a Monomials. Def: A monomial is an expression that is a number, a variable or the product of a number and one or more variables. Constants

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

Page 4: Section 5.1a Monomials. Def: A monomial is an expression that is a number, a variable or the product of a number and one or more variables. Constants

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

Page 5: Section 5.1a Monomials. Def: A monomial is an expression that is a number, a variable or the product of a number and one or more variables. Constants

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

Page 6: Section 5.1a Monomials. Def: A monomial is an expression that is a number, a variable or the product of a number and one or more variables. Constants

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

Page 7: Section 5.1a Monomials. Def: A monomial is an expression that is a number, a variable or the product of a number and one or more variables. Constants

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

Page 8: Section 5.1a Monomials. Def: A monomial is an expression that is a number, a variable or the product of a number and one or more variables. Constants

Simplify

5.

24ab 2

6a 1b 3

6.

(312 )(32)

7.

(2n3)4

Page 9: Section 5.1a Monomials. Def: A monomial is an expression that is a number, a variable or the product of a number and one or more variables. Constants

Homework

Page 259Problems: 19-45 (odd)


Dividing Monomials

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