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# Multiplication Property Exponents

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### Multiplication Property Exponents

1. 1. Multiplication Properties of Exponents 06/01/09 PH 8-6 Bitsy Griffin
2. 2. Multiplying Powers – same base <ul><li>For any nonzero number a and any integers m and n, </li></ul><ul><li>a m ● a n = a m+n </li></ul>06/01/09 PH 8-6 Bitsy Griffin
3. 3. Multiplying Powers – same base <ul><li>8 4 ● 8 2 = 8 2+4 = 8 6 </li></ul><ul><li>8 3 ● 8 3 = 8 3+3 = 8 6 </li></ul><ul><li>3 5 ● 3 4 = 3 5+4 = 3 9 </li></ul><ul><li>6 4 ● 6 -3 = 6 4+-2 = 6 2 </li></ul>06/01/09 PH 8-6 Bitsy Griffin
4. 4. Ex 1 - Simplify the Expressions <ul><li>m 3 ● n 4 ● m 5 </li></ul><ul><li>Rearrange the bases. </li></ul><ul><li>m 3 ● m 5 ● n 4 </li></ul>06/01/09 PH 8-6 Bitsy Griffin
5. 5. Ex 1 - Simplify the Expressions <ul><li>Now follow the rules for multiplying bases. </li></ul><ul><li>m 3 + 5 ● n 4 </li></ul><ul><li>m 8 ● n 4 </li></ul>06/01/09 PH 8-6 Bitsy Griffin
6. 6. Ex 1 - Practice <ul><li>(-5m 2 )(-2m 4 ) </li></ul><ul><li>(-2a 2 b 3 )(3a 4 ) </li></ul><ul><li>(5x 2 y 3 )(-2x 4 y 5 ) </li></ul><ul><li>(3m 2 n 5 )(-8mn 2 ) </li></ul>06/01/09 PH 8-6 Bitsy Griffin
7. 7. Ex 2 – Scientific Notation <ul><li>Use your calculator to help you. Remember that you may or may not have to convert the numbers from standard to scientific. </li></ul>06/01/09 PH 8-6 Bitsy Griffin
8. 8. Ex 2 – Scientific Notation <ul><li>200(5x10 3 )(1x10 7 ) </li></ul><ul><li>8(10x10 11 )(2.5x10 3 ) </li></ul><ul><li>(9x10 8 )(0.2x10 4 ) </li></ul>06/01/09 PH 8-6 Bitsy Griffin
9. 9. Ex 2 – Scientific Notation <ul><li>Suppose you are an astronaut on a mission to Mars. Your spacecraft is traveling at a speed of 2.5 x 10 4 mi/h. It takes you 5.5 x 10 3 h to reach Mars. How many miles do you travel? </li></ul>06/01/09 PH 8-6 Bitsy Griffin
10. 10. Ex 2 – Scientific Notation <ul><li>Set up your problem. </li></ul><ul><li>(2.5 x 10 4 ) (5.5 x 10 3 ) = ? </li></ul>06/01/09 PH 8-6 Bitsy Griffin
11. 11. Ex 3 – Write w/ Positive Exponents <ul><li>Use the same rules you learned for multiplying exponents AND for negative exponents. </li></ul>06/01/09 PH 8-6 Bitsy Griffin
12. 12. Ex 3 – Write w/ Positive Exponents <ul><li>a -5 ● a 3 </li></ul><ul><li>a -5 + 3 </li></ul><ul><li>a -2 </li></ul><ul><li>1 / a 2 </li></ul>06/01/09 PH 8-6 Bitsy Griffin
13. 13. Ex 3 – Practice <ul><li>m 8 ● m – 5 </li></ul><ul><li>(2 a -3 )(5a 4 ) </li></ul><ul><li>(-3p -5 )(2p 8 ) </li></ul><ul><li>1/(x 3 ● x -7 ) </li></ul>06/01/09 PH 8-6 Bitsy Griffin