ExponentsExponents

Multiplying MonomialsMultiplying Monomials

What is does an exponent look What is does an exponent look like?like?

It looks like a little number to the upper It looks like a little number to the upper right of another one…right of another one…

Like this: Like this: 3322

In the number above, the 3 is called the In the number above, the 3 is called the basebase. The two is the . The two is the exponentexponent..

What 3What 322 means. means.

Three times itself twice.Three times itself twice.In numbers it means: 3 x 3.In numbers it means: 3 x 3.

What it does What it does NOTNOT mean mean

3322 does NOT mean 3x2. does NOT mean 3x2.This is a common mistake that students This is a common mistake that students

make.make.

3333 does not mean 6. does not mean 6.Students make the mistake of sometimes Students make the mistake of sometimes

adding the base to the exponent.adding the base to the exponent.

Let’s take a at some Let’s take a at some number sentences that are number sentences that are

equal to bases and equal to bases and exponents.exponents.

What does What does 4422 mean?mean?

4422 = 4*4 = 4*4

443 3 means…means…

4433 = 4*4*4 = 4*4*4

More powers of 4.More powers of 4.

4444 = =

4*4*4*44*4*4*4

4455 = =

4*4*4*4*44*4*4*4*4

Powers of 10Powers of 10101022 = 10*10 = = 10*10 =

100100

101033 = 10*10*10 = = 10*10*10 =10001000

101044 = 10*10*10*10 = = 10*10*10*10 = 10,00010,000

What about a number to the What about a number to the first power?first power?

If 3If 322 is 3*3, 3 is 3*3, 311 is just one 3 is just one 3

4411 = 4 = 4

5511 = =

5 5 5511 does NOT mean 5x1, it is five to the first does NOT mean 5x1, it is five to the first

power.power.

Evaluate 6Evaluate 633

EEvaluvaluatatee means find the value means find the value

6633 = (6x6)*6 = (6x6)*6

(36)*6 = 216(36)*6 = 216

Assign 19-29; 35-49 oddsAssign 19-29; 35-49 odds

#19#192266 = =

(2*2)*(2*2)*(2*2)=(2*2)*(2*2)*(2*2)=

4*4*4 = 16*4 =4*4*4 = 16*4 =#21#21

5533 = 5*5*5= = 5*5*5=

25*5 =25*5 =

Product of PowersProduct of Powers

There’s a quick way to multiply There’s a quick way to multiply numbers in exponential form.numbers in exponential form.

Let’s look at numbers with the Let’s look at numbers with the same base that have exponents.same base that have exponents.

3322 x 3 x 333 = (3*3)*(3*3*3) = (3*3)*(3*3*3)How many threes are there?How many threes are there?

How does five threes relate to the two How does five threes relate to the two exponents : 2 and 3?exponents : 2 and 3?

3322 x 3 x 333 = 3*3*3*3*3 = 3 = 3*3*3*3*3 = 355

Let’s check that out.Let’s check that out.

If 4If 433 * 4 * 455 = (4*4*4)*(4*4*4*4*4) and = (4*4*4)*(4*4*4*4*4) and

(4*4*4)*(4*4*4*4*4) = 4(4*4*4)*(4*4*4*4*4) = 48 8 then we should be then we should be able to add the exponents together.able to add the exponents together.

9922*9*911 = 9 = 933

(9*9)*9 = 81*9 = 729(9*9)*9 = 81*9 = 729

Give your answers in exponential Give your answers in exponential form.form.

2233*2*244

8 * 88 * 833

yy22 * y * y33

3355*3*333

Click on the next slide when you are ready for the answers.Click on the next slide when you are ready for the answers.

Answers in exponential formAnswers in exponential form

2233*2*24 = 4 = 2*2*2*2*2*2*2=22*2*2*2*2*2*2=277

8 * 88 * 833=8*(8*8*8)=8=8*(8*8*8)=844

yy22 * y * y33=(y*y)*(y*y*y) = y=(y*y)*(y*y*y) = y55

3355*3*333 = 3*3*3*3*3*3*3*3 = 3 = 3*3*3*3*3*3*3*3 = 388

Click on the next slide when you are ready for the answers.Click on the next slide when you are ready for the answers.

Multiplication of MonomialsMultiplication of Monomials

What is a monomial?What is a monomial?

A monomial is an algebraic expression A monomial is an algebraic expression that is either a…that is either a…ConstantConstantVariable, orVariable, orA product of a constant and one or more A product of a constant and one or more

variables.variables.

Examples of monomialsExamples of monomials

A monomial is an algebraic expression A monomial is an algebraic expression that is either a…that is either a…Constant – 4 18 32 2Constant – 4 18 32 2Variable – x y m nVariable – x y m nA product of a constant and one or more A product of a constant and one or more

variables. 4xy 3mn 3n 8x 12yvariables. 4xy 3mn 3n 8x 12y

Multiplication of MonomialsMultiplication of Monomials

Use the commutative and associative Use the commutative and associative properties of multiplication to your properties of multiplication to your advantage.advantage.

Oftentimes it works well to separate your Oftentimes it works well to separate your coefficients and variables, such as..coefficients and variables, such as..

Let’s simplify 4aLet’s simplify 4a22b * 3 abb * 3 ab33

4a4a22b * 3 abb * 3 ab33

= 4*a*a*b*3*a*b*b*b= 4*a*a*b*3*a*b*b*b

=4*3*a*a*a*b*b*b*b =4*3*a*a*a*b*b*b*b

= 12a= 12a33bb44

Try someTry some

(5t)(20t(5t)(20t33)=)=

(4m(4m22)(-16mn)(-16mn22)=)=

Answers on the next slide…Answers on the next slide…

AnswersAnswers

(5t)(20t(5t)(20t33)=5*t*20*t*t*t =5*20*t*t*t*t=100t)=5*t*20*t*t*t =5*20*t*t*t*t=100t44

(4m(4m22)(-16mn)(-16mn22)=4*m*m*(-16)*m*n*n=)=4*m*m*(-16)*m*n*n=

4*(-16)*m*m*m*n*n=4*(-16)*m*m*m*n*n=

-64m-64m33nn22