1. P ROPERTIES OF E XPONENTS Algebra Seminar 2012-2013

2. M ULTIPLYING W ITH S AME B ASE Multiply. Write the product as one power. A. 6 6 6 3 B. n 5 n 7 C. 2 5 2 D. 24 4 24 4

3. M ULTIPLYING 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 Words NumbersAlgebra MULTIPLYING POWERS WITH THE SAME BASE

4. M ULTIPLYING W ITH D IFFERENT B ASE A. x 5 y 2 B. 41 2 42 7 When the bases are different, we can NOT combine them. C. b 6 h 4 D. -4 5 -9 3 None of these examples can be simplified any further, so they need to stay the way they are.

5. L ET ’ S TRY S OME …

6. D IVIDING Divide. Write the product as one power. 7 5 7 3 A. x 10 x 9 B. 9 9 9 2 C. D. e 10 e 5

7. D IVIDING Notice what occurs when you divide powers with the same base. 5 5 5353 = 5  5  55  5  5 5  5  5  5  5 = 5 5 = 5 2 = 5  5  55  5  5 5  5  5  5  5 DIVIDING POWERS WITH THE SAME BASE WordsNumbersAlgebra To divide powers with the same base, keep the base and subtract the exponents. 6 5 6 9 – 4 6 9 6 4 = = b m – n b m b n =

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9. T HE Z ERO P OWER WordsNumbers Algebra The zero power of any number except 0 equals 1. 100 0 = 1 (–7) 0 = 1 a 0 = 1, if a  0