Download Math 95 Section 5.1 and 5.2 Rules of Exponents Blank.notebook

Math 95 Section 5.1 and 5.2 Rules of Exponents Blank.notebook
January 24, 2017
Sections 5.1 and 5.2
Exponents
﴾We are not doing Scientific Notation﴿
Objectives:
• Use the product rule for exponents
• Evaluate expressions raised to the zero power
• Use the quotient rule for exponents
• Evaluate expressions raised to the negative nth power
• Use the power rule for exponents
• Use exponent rules to and definitions to simplify
exponential expressions
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Math 95 Section 5.1 and 5.2 Rules of Exponents Blank.notebook
January 24, 2017
Exponents:
Exponents: a shorthand way of writing...
x is the
and 4 is the
It means:
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Math 95 Section 5.1 and 5.2 Rules of Exponents Blank.notebook
January 24, 2017
Exponents:
Product rule for exponents:
If m and n are positive integers and a is a real number, then:
Or:
To multiply two powers with the same base, add their exponents.
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Math 95 Section 5.1 and 5.2 Rules of Exponents Blank.notebook
January 24, 2017
The Product Rule for Exponents:
Product rule for exponents:
If m and n are positive integers and a is a real number, then:
Only simplify one thing at a time—and show every step. You’ll make fewer mistakes.
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Math 95 Section 5.1 and 5.2 Rules of Exponents Blank.notebook
January 24, 2017
Exponents:
Power Rules for Exponents:
If a and b are real numbers and m and n are integers, then:
Power rule
Power of a product
Power of a quotient
Or:
To raise a power to a power, multiply the exponents.
To raise a product/quotient to a power, distribute the exponents.
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Math 95 Section 5.1 and 5.2 Rules of Exponents Blank.notebook
January 24, 2017
The Power Rule for Exponents:
Power Rule for Exponents:
If a and b are real numbers and m and n are integers, then:
Remember:
Only simplify one thing at a time—and show every step. You’ll make fewer mistakes.
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Math 95 Section 5.1 and 5.2 Rules of Exponents Blank.notebook
January 24, 2017
Exponents:
Quotient Rule for Exponents:
If a is a nonzero real number and m and n are both integers, then:
Or:
To divide powers with the same base, subtract the exponent in the denominator
from the exponent in the numerator.
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Math 95 Section 5.1 and 5.2 Rules of Exponents Blank.notebook
January 24, 2017
The Quotient Rule for Exponents:
Quotient Rule for Exponents:
If a is a nonzero real number and
m and n are both integers, then:
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Math 95 Section 5.1 and 5.2 Rules of Exponents Blank.notebook
January 24, 2017
Exponents:
Zero Exponent:
If a does not equal zero then:
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Math 95 Section 5.1 and 5.2 Rules of Exponents Blank.notebook
January 24, 2017
Zero Exponent:
Zero Exponent:
If a does not equal zero then:
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Math 95 Section 5.1 and 5.2 Rules of Exponents Blank.notebook
January 24, 2017
Exponents:
Negative Exponents:
If a is a real number other than 0 and n is a positive integer, then:
Or:
To raise a base to a negative power, write the reciprocal of the base and
make the exponent positive.
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Math 95 Section 5.1 and 5.2 Rules of Exponents Blank.notebook
January 24, 2017
Negative Exponents:
Negative Exponents:
If a is a real number other than 0 and n is a positive integer, then:
Only negative exponents move, not negative coefficients
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Math 95 Section 5.1 and 5.2 Rules of Exponents Blank.notebook
January 24, 2017
Negative Exponents:
Negative Exponents:
If a is a real number other than 0 and n is a positive integer, then:
Only negative exponents move, not negative coefficients
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Math 95 Section 5.1 and 5.2 Rules of Exponents Blank.notebook
January 24, 2017
The Properties of Exponents:
If a and b are real numbers and m and n are integers, then:
Product rule
Zero Exponent
Negative Exponent
Quotient Rule
Power rule
Power of a product
Power of a quotient
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Math 95 Section 5.1 and 5.2 Rules of Exponents Blank.notebook
January 24, 2017
Practice Exponents:
Simplify completely. Write with positive exponents only.
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Math 95 Section 5.1 and 5.2 Rules of Exponents Blank.notebook
January 24, 2017
Simplifying Exponents:
The Rule
Not Yet Simplified
Simplified
No more negative exponents
The numbers in the fraction
are simplified
Numbers raised to powers
are evaluated
Zero should not be seen as
an exponent
If variables appear more than
once, combine them
No more parentheses
Factors should be combined
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