6.3laws of exponents.notebook

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ExponentsExponents

Power

Base

Exponentx3 =x x x 53 =5 5 5

An exponent tells how many times a number, the base, is used as a factor. A power has two parts, a base and an exponent.

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6.3: 

ExponentsExponentsDownload video from youtube

http://www.youtube.com/watch?v=dQ9A­o3dUlM

6.3laws of exponents.notebook

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May 12, 2015

ExponentsExponentsDownload video from youtube

 http://www.youtube.com/watch?v=QIZTruxt2rQ

Laws of ExponentsLaws of ExponentsZero Exponents

Negative Exponents

Multiplying Exponents

Dividing Exponents

Power-To-Power Exponents

6.3laws of exponents.notebook

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(xyz)0Laws of ExponentsLaws of Exponents

Zero Exponents

Any power which has an exponent of zero is always..... 1

x 0

50

Laws of ExponentsLaws of ExponentsNegative Exponents

x -2 is an "unsimplified power".

All negative exponents must be simplified and become positive exponents. There is a positive position and negative position in the numerator and denominator.

x-2

x2

x2

x-2

6.3laws of exponents.notebook

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Laws of ExponentsLaws of ExponentsNegative Exponents

(Arrange the powers so there are NO negative exponentsand arrange variables in alphabetical order)

y-2

y2 x2

x-2

4z-1

z

a5

a-5 b-2

b2

ee-1

d-5

d5

-5-1

-5f7

f-7

m-4

m4 n-3

n3 33-1

Place in simplified form.

Place in simplified form.

gg2

h-1

hk-8

k8

1. z -4

2. 270 4. (5x)0

5. a-4 b2c

Laws of ExponentsLaws of ExponentsPRACTICE MAKES PERFECT!

Simplify the expressions. All negative exponents must be positive.

3. 2x2

4m-4n2 6. 2-1x2

m-4n2

6.3laws of exponents.notebook

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Laws of ExponentsLaws of ExponentsMultiplying Exponents

• Bases must be equal.• Exponents add together.• xa • xb = xa+b

Laws of ExponentsLaws of ExponentsMultiplying Exponents

b4 • b-1 = b4+-132 • 35 = 32+5

= b3= 37=2187

m3n4 • mn2 = m3+1n4+2 = m4n6

2x3 • 4x2 = 2•4•x3+2 = 8b3

6.3laws of exponents.notebook

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Laws of ExponentsLaws of ExponentsPRACTICE MAKES PERFECT!

Simplify the expressions. All negative exponents must be positive.

1. (a2)(b3)

2. (2)(c3)(d3)(c4)

3. 5m-5n3p-1 • 2m4p2

4. (2)(a3b4)(b-1c4)

5. 2m5n3 • 2-1m2n2

6. 2x2y3z • 3x4 • y5z2

Laws of ExponentsLaws of ExponentsDividing Exponents

• Bases must be equal.• Exponents subtract each other.• xa 1 xa = xa-b

xb = xb-a xb 1or

6.3laws of exponents.notebook

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2 4

2x2y7

4x4y3

Laws of ExponentsLaws of ExponentsDividing Exponents

b3

b2 = b3-2

1 = b1 b

14c-2d5

6c-7d

= = 1y7-3

2x4-2 = y4

2x2

14 6

= = 7c-2-(-7)

3d5-2 =14c5

3d3

Laws of ExponentsLaws of ExponentsPRACTICE MAKES PERFECT!

Simplify the expressions. All negative exponents must be positive.

1. 2x2

4x-4y2 3. x2y3z2

x5y2z7

2. 2-3a2c3 22a-4b2

3. g2h3

g5h5k-2

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Laws of ExponentsLaws of ExponentsPower to Power Exponents

Mark all exponential values so they show the exponential form. (If it does not have an exponent, insert a “1” to represent the exponent.)

Laws of ExponentsLaws of ExponentsPower to Power Exponents

Follow the distribution rule – Distribute through multiplication from the exponent outside the parenthesis to the exponent inside the parenthesis. Every value inside the parenthesis must have an exponent attached!!!Exponent on the outside of the parenthesis multiplies (times) all inside EXPONENTS.

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Laws of ExponentsLaws of ExponentsPower to Power Exponents

When you have a fraction – remember to distribute to the numerator as well as the denominator.

  2x5    3m3n7  

  21 3x5 3    m3 3n7 3  

• •

• •

  83x15     m9 n21   

Laws of ExponentsLaws of ExponentsPRACTICE MAKES PERFECT!

Simplify the expressions. All negative exponents must be positive.

1. (ab-4)2

2. (2c3df3)3

3. 2x2 2

m-4n2

4. (5x)-2

5. (a3b2c)4

6. (4a-2b3c)-3