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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
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