Laws of Exponents

Laws of Exponents

Lesson objectives Teachers' notes

1) To understand what exponents are.

2) To understand the laws of zero, negative, multiplying, dividing, and power to power exponents.

Laws of Exponents

Base

Power

baseAn exponent tells how many times a number, the

, is used as a factor. A power has two parts, a base and an exponent.

{{x3 =x.x.x Exponent

53 =5.5.5

Exponents

Laws of Exponents

Laws of ExponentsZero Exponents

Negative Exponents

Multiplying Exponents

Dividing Exponents

Power-To-Power Exponents

Laws of Exponents

Laws of ExponentsZero Exponents

Any power which has an exponent of

z

(ero i

xs always

y...

1x 0

50

Laws of Exponents

Laws 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

x-2

Laws of Exponents

Laws of ExponentsMultiplying Exponents

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

Laws of Exponents

Laws of Exponents Multiplying Exponents

32 • 35

b4 • b-1

m3n4 • mn2

2x3 • 4x2

Laws of Exponents

Laws of ExponentsDividing Exponents

• Bases must be equal. • Exponents subtract each other.

Laws of Exponents

2x2y7

Laws of Exponents Dividing Exponents

b3

b2

4x4y3

14c-2 d5

6c-7 d

Laws of Exponents

Laws 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 Exponents

Laws of ExponentsPower to Power Exponents

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

32x5

m3n7

Laws of Exponents

Laws of exponents

PRACTICE 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