8.3 – Multiplying Exponents Warm Up Write each expression using an exponent. 1. 2 • 2 • 2 2. x • x • x • x 3. Write each expression without using an exponent. 4. 43 5. y2 6. m–4 23 4 • 4 • 4 y • y

Lesson #8.3 Multiplying Exponents Objective: SWBAT multiply powers. Concept: Unit 8

8.3 – Multiplying Exponents Given Think of it like this: x * x * x * x * x * x * x

Property: Multiply Powers with the Same Base RULE: the bases MUST be the same

8.3 – Multiplying Exponents Products of powers with the same base can be found by writing each power as a repeated multiplication. Notice the relationship between the exponents in the factors and the exponents in the product 5 + 2 = 7.

8.3 – Multiplying Exponents Simplify. A. Since the powers have the same base, keep the base and add the exponents. B. Group powers with the same base together. Add the exponents of powers with the same base.

8.3 – Multiplying Exponents Simplify. C. Group powers with the same base together. Add the exponents of powers with the same base. D. Group the positive exponents and add since they have the same base 1 Add the like bases.

8.3 – Multiplying Exponents A number or variable written without an exponent actually has an exponent of 1. Remember! 10 = 101 y = y1

8.3 – Multiplying Exponents Simplify. a. Since the powers have the same base, keep the base and add the exponents. b. Group powers with the same base together. Add the exponents of powers with the same base.

8.3 – Multiplying Exponents Simplify. c. Group powers with the same base together. Add.

8.3 – Multiplying Exponents Simplify. d. Group the first two and second two terms. Divide the first group and add the second group. Multiply.

8.3 – Multiplying Exponents Examples: a. b. c.

8.3 – Multiplying Exponents Multiplying powers in algebraic expressions When multiplying, only combine the things that are similar. Example: you can rewrite it as or

8.3 – Multiplying Exponents Try:

Lesson #8.4 Properties for Multiplying Exponents Objective: SWBAT raise a power to a power and raise a product to a power. Concept: Unit 8

8.4 – More Multiplying Exponents To find a power of a power, you can use the meaning of exponents. Notice the relationship between the exponents in the original power and the exponent in the final power:

8.4 – More Multiplying Exponents

8.4 – More Multiplying Exponents Simplify. Use the Power of a Power Property. Simplify. Use the Power of a Power Property. Zero multiplied by any number is zero 1 Any number raised to the zero power is 1.

8.4 – More Multiplying Exponents Simplify. C. Use the Power of a Power Property. Simplify the exponent of the first term. Since the powers have the same base, add the exponents. Write with a positive exponent.

8.4 – More Multiplying Exponents Simplify. Use the Power of a Power Property. Simplify. Use the Power of a Power Property. Zero multiplied by any number is zero. Any number raised to the zero power is 1. 1

8.4 – More Multiplying Exponents Simplify. Use the Power of a Power Property. c. Simplify the exponents of the two terms. Since the powers have the same base, add the exponents.

8.4 – More Multiplying Exponents Powers of products can be found by using the meaning of an exponent.

8.4 – More Multiplying Exponents Simplify. A. Use the Power of a Product Property. Simplify. B. Use the Power of a Product Property. Simplify.

8.4 – More Multiplying Exponents Simplify. C. Use the Power of a Product Property. Use the Power of a Product Property. Simplify.

8.4 – More Multiplying Exponents Simplify. Use the Power of a Product Property. Simplify. Use the Power of a Product Property. Use the Power of a Product Property. Simplify.

8.4 – More Multiplying Exponents Simplify. c. Use the Power of a Product Property. Use the Power of a Product Property. Combine like terms. Write with a positive exponent.

8.4 – More Multiplying Exponents Simplify. 1. 32• 34 3. 5. 7. 2. (x3)2 4. 6.

8.4 – More Multiplying Exponents 7. The islands of Samoa have an approximate area of 2.9  103 square kilometers. The area of Texas is about 2.3  102 times as great as that of the islands. What is the approximate area of Texas? Write your answer in scientific notation.