2.1 Properties of Exponents.notebook
September 29, 2016
Warm Up
Solve each quadratic equation using each method once.
1. (x ­ 3)2 + 12 = 0
2. x2 ­ 25 = 0
3. 2x2 = 12x + 32
4. 3x2 ­ 19x + 20 = 0 Jan 28­5:48 PM
2.1 Properties of Exponents
I. Product Properties
am an = am + n
To multiply two powers (product of powers): • must have the same base • add the exponents
(am)n = amn
To find a power of a power: • multiply the exponents
(a b)m = am bm
To find the power of a product: • raise each factor to the power (distribute the exponent outside the parentheses to every exponent inside the parentheses).
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2.1 Properties of Exponents.notebook
September 29, 2016
Simplify.
1.
(6x2y3)(xyz)
2.
(2ab2)(­4a3b3c)
3.
(­2r2s)3
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IMPORTANT!!!
To simplify means:
• there is only one coefficient.
• each base appears only once in the answer.
• all exponents are positive.
• all fractions are reduced.
4.
5.
6.
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2.1 Properties of Exponents.notebook
September 29, 2016
II. Quotient Properties
To divide two powers (quotient of powers): • again must have the same base • subtract the exponents
To find the power of a quotient: • raise the numerator to the power • raise the denominator to the power
• divide (reduce, if possible)
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Simplify.
1.
2.
3.
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2.1 Properties of Exponents.notebook
September 29, 2016
Simplify.
4.
5.
6.
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III. Zero Exponent Property
A non­zero number raised to the zero power is one!!!
NOTE:
is undefined.
EXAMPLES:
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2.1 Properties of Exponents.notebook
September 29, 2016
IV. Negative Exponent Properties
A negative exponent means a reciprocal.
Example:
Example:
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