Exponent Properties: The Product Rule. 2. Exponential expressions multiplied with each other that have the same base.

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Jacob Hunt
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1 Exponent Properties: The Product Rule 1. What is the difference between 3x and x 3? Explain in complete sentences and with examples. 2. Exponential expressions multiplied with each other that have the same base. Product Repeated Multiplication Power of the form a b 2 2 (2 3 ) 2 * 2 * 2 * 2 * (3 5 ) 11 6 (11 8 ) 5 1 * 5 4 * 5 3 X 3 * X 4 3. Now, explain a general rule for what happens when we have two exponential expressions multiplying each other with the same bases. You can write the rule in words, or use an example or expression to communicate the rule. 4. Why do you think this rule is called the product rule? 5. Write the algebraic rule for this concept.

2 1. What does it mean to distribute? Product Exponent Properties: The Distributive Rule for Products Repeated Multiplication Rearrange the multiplications using the commutative property, so similar things are next to each other. Power of the form a c * b c (2 * 3) 3 (2*3) (2*3) (2*3) 2 *2*2*3*3* (4*6) 4 (x*y) 5 (3*4*5) 2 (3x) 6 2. Now, explain a general rule for what happens when we have two exponential expressions multiplying each other with the same bases. You can write the rule in words, or use an example or expression to communicate the rule. 3. Why do you think this rule is called the distributive rule? 4. How is this rule different from the product rule? 5. Write the algebraic rule for this concept.

3 1. What does the term quotient mean? Exponent Properties: The Quotient Rule Quotient Repeated Multiplication Cancel out Power of the form A b 2 3 2*2* *2 2*2*2 2* X 10 X y 20 Too big to write out? Find another way! 5 7 y 8 A 7 b Now, explain a general rule for what happens when we have two exponential expressions dividing each other with the same base. You can write the rule in words, or use an example or expression to communicate the rule. 3. Write the algebraic rule for this concept.

4 Exponent Properties: The Zero Exponent Rule 1. Why does a zero exponent result in an answer of 1? Quotient X 20 X 20 Use the quotient rule to write in the form a b Look at the original quotient. What is the result as just a number? 2. What do you think any rational number to the zero power should equal? Write an expression to demonstrate your answer.

5 Exponent Properties: The Distributive Rule for Quotients 1. Quotient Repeated Multiplication Write as a fraction 2. Now, determine a general rule for what happens when we have a quotient raised to a power. You may want to write the rule in words, or you can use an example or expression to communicate the rule. 3. Why is this rule called the distributive rule for exponents? 4. Write the algebraic rule for this concept.

6 Exponent Properties: The Power Rule 1. What information have you already learned that helps explain a power to a power? Problem to simplify First repeated multiplication Second repeated multiplication Power of the form A c (2 2 ) * 2 2 2*2*2*2 2 4 (5 3 ) 4 X 6 * x 6 * x 6 * x (3 5 y 2 ) 3 (a 20 ) 32 Too big to write out? Find another way 2. Now, determine a general rule for what happens when we have something already to a power, raised to a power again. You may want to write the rule in words, or you can use an example or expression to communicate the rule. How is this rule different from the product rule? 3. How is this rule different from the product rule? 4. Write the algebraic rule for this concept.

7 Exponent Properties: Negative Exponents 1. Quotient Repeated Multiplication Answer as a fraction Use the quotient rule to get power of the form a c * *2*2*2*2 a 4 a a 4 b 5 a 9 b x*x*x*y x*x*x*x*x*x*x = What does a negative exponent mean? Look at the two columns on the right and try to formulate a rule. 3. Are positive expressions with negative exponents negative? 4. What do you think this simplifies to be? 1_ Go ahead and take a guess or try to work it out mathematically Write the algebraic rule for this concept.

Objective Simplify expressions using the properties of exponents.

Pre-Algebra: Exponent Properties Objective Simplify expressions using the properties of exponents. Exponents are used to simplify expressions. For example, a*a*a*a*a*a*a is the expanded expression of a