1. Pre-Algebra 2-7 Properties of Exponents Multiplication of Exponents Rules for multiplying with exponents

2. Pre-Algebra 2-7 Properties of Exponents The factors of a power, such as 7 4, can be grouped in different ways. Notice the relationship of the exponents in each product. 7 7 7 7 = 7 4 (7 7 7) 7 = 7 3 7 1 = 7 4 (7 7) (7 7) = 7 2 7 2 = 7 4

3. Pre-Algebra 2-7 Properties of Exponents Words NumbersAlgebra To multiply powers with the same base, keep the base and add the exponents. b m b n = b m + n 3 5 3 8 = 3 5 + 8 = 3 13 MULTIPLYING POWERS WITH THE SAME BASE

4. Pre-Algebra 2-7 Properties of Exponents Additional Example 1A & 1B: Multiplying Powers with the Same Base A. 6 6 6 3 6 9 6 6 + 3 B. n 5 n 7 n 12 n 5 + 7 Add exponents. Multiply. Write the product as one power.

5. Pre-Algebra 2-7 Properties of Exponents D. 24 4 24 4 C. 2 5 2 2 6 2 5 + 1 24 8 4 + 4 Think: 2 = 2 1 Additional Example 1: Multiplying Powers with the Same Base Continued Multiply. Write the product as one power. Add exponents.

6. Pre-Algebra 2-7 Properties of Exponents Try This: Example 1A & 1B A. 4 2 4 4 4 6 4 2 + 4 B. x 2 x 3 x 5 x 2 + 3 Add exponents. Multiply. Write the product as one power.

7. Pre-Algebra 2-7 Properties of Exponents D. 41 2 41 7 C. x 5 y 2 41 9 2 + 7 Try This: Example 1C & 1D Multiply. Write the product as one power. Cannot combine; the bases are not the same. Add exponents. x 5 y 2

8. Pre-Algebra 2-7 Properties of Exponents Simplify. Example 1: Finding Products of Powers 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.

9. Pre-Algebra 2-7 Properties of Exponents Simplify. Example 1: Finding Products of Powers C. D. 1 Group powers with the same base together. Add the exponents of powers with the same base. Group the positive exponents and add since they have the same base Add the like bases.

10. Pre-Algebra 2-7 Properties of Exponents

11. Pre-Algebra 2-7 Properties of Exponents Simplify. Example 3: Finding Powers of Powers Use the Power of a Power Property. Simplify. 1 Use the Power of a Power Property. Zero multiplied by any number is zero Any number raised to the zero power is 1.

12. Pre-Algebra 2-7 Properties of Exponents Simplify. Example 3: Finding Powers of Powers 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. C.

13. Pre-Algebra 2-7 Properties of Exponents Check It Out! Example 3 Simplify. Use the Power of a Power Property. Simplify. 1 Use the Power of a Power Property. Zero multiplied by any number is zero. Any number raised to the zero power is 1.

14. Pre-Algebra 2-7 Properties of Exponents Check It Out! Example 3c Simplify. Use the Power of a Power Property. Simplify the exponents of the two terms. Since the powers have the same base, add the exponents. c.