Using Properties of Exponents EQ: How do we use properties of exponents? Monday, July 14, 2014 M2 Unit 5a: Day 1
Properties of Exponents Let a and b be real numbers and let m and n be integers. Product of Powers Property Power of a Power Property Power of a Product Property Zero Exponent Property Quotient of Powers Property Power of Quotient Property Negative Exponent Property
Product of Powers: To multiply powers with the same base, add the exponents and keep the common base. • Examples: a. b.
Your turn: 1. 2. 3. Keep common bases Add the exponents
Power of a Power: To raise a power to a power, keep the base and multiply the exponents. • Examples: a. b.
Your turn: 1. 2. 3. Keep The Base Multiply The Exponents
Power of a Product: To raise a product to a power, raise each factor to the power. • Examples: a. b. Simplify any numeric bases raised to exponents This should remind you of the distributive property. Remember to “distribute” the exponent to each base, numeric and variable! Warning: No distributing over addition!!!
Your turn: 1. 2. 3. Raise Each Factor To The Power It’s Like The Distributive Property
Zero Exponent: Any number raised to the zero power is equal to “1”. • Examples: a. b.
Your turn: 1. 2. 3. Anything Raised To The Zero Power =1
Quotient of Powers: To divide powers with the same base, subtract the exponents and keep the common base. Also, remember that common factors cancel out! • Examples: a. b. Keep the base where the exponent is larger
Your turn: 1. 2. 3. Common Factors Cancel Out With Common Bases Subtract Exponents
Power of Quotient: To raise a quotient to a power, raise the numerator and the denominator to the power. • Examples: a. b.
Raise the numerator and denominator to the power Your turn: 1. 2. 3. Simplify any factors with numeric bases
Negative Exponent Property: • You may want to think of it this way: unhappy ( ) exponents will become happy ( ) by having the base/exponent pair “switch floors”! • Example: A.) B.) positive negative
You try: 1. 2. 3. 4.
Simplifying Exponential Expressions To simplify exponential expressions completely: Get rid of parentheses Get rid of negative exponents Make sure there is only one of each base Cancel out common factors
Simplify the exponential expression. multistep C. Examples: A. B. D.
You try: multistep 1. 2. 3. 4.
A. B. C. D. multistep Simplify the exponential expression.
You Try:5.6. 7. multistep