Multiplying Monomials

Multiplying Monomials

Figure these out on your calculator: 4 = 64 3

5 = 3125 5

Now, try to figure these out:

(4 )(4 ) = 16384 2 5 (4 )(4 ) = 16384 7 16384 (4 ) = 3

4

How did you type it in??

Look at the exponents

Try These: 3 ● x = 3x

3 ● 4 ●x ● y = 12xy

5 ● y = 5y

x ● x ● x = x³

x ● x = x²

g ● g ● x = g²x

These are all MONOMIALS

Now multiply these: x² • x² = x² • x³ = x³ • y² =

(x • x) • (x • x) =

x4

(x • x) • (x • x • x) =

x5

(x • x • x) • (y • y) =

x3y2

EXPONENT RULE #1: Whenare multiplying If the numbers or variables NOT the the same with exponents, same, younumbers can’t mess with the just add the exponents. exponents ! You just leave them…

ON your classwork paper:

Write the problems and simplify them: 1. (x5)(x1)= 2. (x2y1)(y3)= 3. (x6y3z)(y2z3)= 4. (3x)(2x)= 5. (3xy2)(2x4y5)=

Sometimes, there will be an exponent of an exponent. Check it out:

(x ) = (x•x•x) = 3 4

4

(x•x•x)•(x•x•x)•(x•x•x)•(x•x•x) =

x

12

EXPONENT RULE #2: When you have an exponent of an exponent, you can just multiply them.

When dealing with normal numbers in with the variables, just treat them normally.

(3x y ) = 3 x y 5 3 4

4 20 12

=81x y

20 12

On your classwork paper: 6.

(xy3)2 =

7.

(3x4)3 =

8.

(4xy3)(2x)3 =

9.

(3x4y2)2(x7) =

10.

(5a3b5c7)4 =

Recall:Monomial: a number or a variable or a bunch grouped together. EXAMPLES OF MONOMIALS: 3 x² 4xy 45x³y² x5y7z3

IF A GROUP INVOLVES adding or subtracting or division, then it is NOT a Monomial !

Dividing Exponents Remember when multiplying the same number that has exponents, you add them.