Warm Up Evaluate. Course Properties of Exponents b 2 for b = 4 4. n 2 r for n = 3 and r =

Learn to apply the properties of exponents and to evaluate the zero exponent. Course 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. Course Properties of Exponents = 7 4 (7 7 7) 7 = = 7 4 (7 7) (7 7) = = 7 4

Course 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 13 MULTIPLYING POWERS WITH THE SAME BASE

Additional Example 1A & 1B: Multiplying Powers with the Same Base Course Properties of Exponents A B. n 5 n 7 n 12 n Add exponents. Multiply. Write the product as one power.

D C Course Properties of Exponents Think: 2 = 2 1 Additional Example 1: Multiplying Powers with the Same Base Continued Multiply. Write the product as one power. Add exponents.

Try This: Example 1A & 1B Course Properties of Exponents A B. x 2 x 3 x 5 x Add exponents. Multiply. Write the product as one power.

Course Properties of Exponents Notice what occurs when you divide powers with the same base. DIVIDING POWERS WITH THE SAME BASE WordsNumbersAlgebra To divide powers with the same base, keep the base and subtract the exponents – = = b m – n b m b n = = 5  5  55  5  5 5  5  5  5  5 = 5 5 = 5 2 = 5  5  55  5  5 5  5  5  5  5

Remember Multiply: add exponents Divide: subtract exponents

Course Properties of Exponents Subtract exponents – Additional Example 2: Dividing Powers with the Same Base Divide. Write the product as one power. A. x 10 x 9 B. Subtract exponents. x 10 – 9 x Think: x = x 1

Course Properties of Exponents Subtract exponents – Try This: Example 2 Divide. Write the product as one power. A. B. e 10 e 5 Subtract exponents. e 10 – 5 e 5

Course Properties of Exponents THE ZERO POWER WordsNumbers Algebra The zero power of any number except 0 equals = 1 (–7) 0 = 1 a 0 = 1, if a  0 Anything to the zero power equals 1

When you have a negative exponent, take the reciprocal and make the exponent positive. Course Properties of Exponents Negative Exponents

Course Properties of Exponents Lesson Quiz: Part 1 Write the product or quotient as one power n 7 1. n 3  n t t 9 t 7

Course Properties of Exponents A school would like to purchase new globes. They can get six dozen for $ from Company A. From Company B, they can buy a half gross for $ Which company should they buy from? (1 gross = 12 2 items) Lesson Quiz: Part 2 Company A 6.