Exponents

Location of Exponent

• An exponent is a little number high and to the right of a regular or base number.

3 4Base

Exponent

Definition of Exponent

• An exponent tells how many times a number is multiplied by itself.

3 4Base

Exponent

What an Exponent Represents

• An exponent tells how many times a number is multiplied by itself.

34= 3 x 3 x 3 x 3

How to read an Exponent

• This exponent is read three to the fourth power.

3 4Base

Exponent

How to read an Exponent

• This exponent is read three to the 2nd power or three squared.

3 2Base

Exponent

How to read an Exponent

• This exponent is read three to the 3rd power or three cubed.

3 3Base

Exponent

What is the Exponent?

2 x 2 x 2 = 23

What is the Exponent?

3 x 3 = 3 2

What is the Exponent?

5 x 5 x 5 x 5 = 54

What is the Base and the Exponent?

8 x 8 x 8 x 8 = 8 4

What is the Base and the Exponent?

7 x 7 x 7 x 7 x 7 =7 5

What is the Base and the Exponent?

9 x 9 = 9 2

How to Multiply Out an Exponent to Find the

Standard Form

= 3 x 3 x 3 x 33

927

81

4

What is the Base and Exponentin Standard Form?

4 2= 16

What is the Base and Exponentin Standard Form?

2 3= 8

What is the Base and Exponentin Standard Form?

3 2= 9

What is the Base and Exponentin Standard Form?

5 3= 125

Product law:

add the exponents together when multiplying the powers with the same base.

Ex:NOTE:

This operation can only be done if the base is the same!

15

312

312

3

3

3*3

Quotient law

subtract the exponents when dividing the powers with the same base.

Ex: NOTE:

This operation can only be done if the base is the same!9

312

312

3

3

33

Power of a power:

keep the base and multiply the exponents.

Ex:

15

5*3

53

4

4

)4(

NOTE:

Multiply the exponents, not add them!

Zero exponent law:

Any power raised to an exponent of zero equals one.

Ex:

1

2141234123483 0

NOTE:

No matter how big the number is, as long as it has zero as an exponent, it equals to one. Except 100

Negative exponents:

To make an exponent positive, flip the base.

Ex:

4096

1

8

1

84

4

NOTE:

This does not change the sign of the base.

Multiplying Polynomials:

In multiplying polynomials, you have to multiply the coefficients and add up the exponents of the variables with the same base.

Ex:

35

3

2

5

32

232

20

*

*

20

5*4

45

yx

y

yy

x

xx

yxyx

Dividing polynomials:

When dividing polynomials, you must divide the coefficients(if possible) and subtract the exponents of the variables with the same base.

Ex:

2

2

24

45

24

45

5

5

525

5

25

xy

y

yy

x

xx

yx

yx

Please simplify the following equations:

Answer:5x

How?:5

32

32 * xx

Please simplify the following equations:

Answer:

513 xx

8x

How?: 8

513

Please simplify the following equations:

Answer:

How?:

255

9765625

510

9765625

5

10

5*2

10

Please simplify the following equations:

Answer:

How?:

35

125

1

5

13

125

1

5

1

5

1

5

1

5

1

53

3

Please simplify the following equations:

)3)(4( 3224 yxyx

Answer:5612 yx

How?:

56

5

32

6

24

12

*

*

12

3*4

yx

y

yy

x

xx

Please simplify the following equations:

22

43

4

12

yx

yx

Answer: 23xy

How?:

2

24

23

3

3

412

xy

yy

x

xx

Review

Copy and complete each of the following questions.

•1.) b2 * b7 •1.) b9 •2.) (p3)4 •2.) p12 •3.) (a2)3 * a3 •3.) a9

•4.) x2 * (xy)2 •4.) x4y2 •5.) (4m)2 * m3

•5.) 16m5 •6.) (3a)3*(2p)2

•6.) 108a3p2

•7.)82*(xy)2*2x •7.) 128x3y2 •8.) w3 * (3w)4 •8.) 81w7 •9.) q0 •9.) 1

•10.) p-2 •10.) 1/p2 •11.)(a2b)0 •11.) 1 •12.)(x-2y3)-2

•12.) x4/y6

•13.) p4

p2 •13.) p2 •14.) 3b2

9b5 •14.) 1/3b3

•15.) (4x2)2

4x4 •15.) 4

•16.) x2 * y0 * 32 x3 * y-4

•16.) 9y4/x

•17.) m 3 * m2n-4 n

•17.) m5/n7 •18.) 3a2 3 2b-1

b * 32 * a •18.) 6a5/b4

•19) (3/4)3 •19) 27/64 •20) 2+3(4)2 •20) 50