More Multiplication Properties Exponents
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The document discusses properties of exponents when raising powers and products to powers. It states that (a^m)^n = a^mn for any nonzero number a and integers m and n. It also states that (ab)^n = a^n b^n for any nonzero numbers a and b and integer n. Several examples are worked out applying these properties. The document also discusses applying exponents to expressions with variables and simplifying.
More Multiplication Properties Exponents
- 1. More Multiplication Properties of Exponents 06/01/09 PH 8-7 Bitsy Griffin
- 2. Raising Powers to Powers For any nonzero number a and any integers m and n, (a m ) n =a mn (5 4 ) 2 =5 8 06/01/09 PH 8-7 Bitsy Griffin
- 3. Raising Powers to Powers (2 3 ) 2 (h 2 ) 4 (3 3 ) 4 (x 3 ) 6 c 5 (c 3 ) 2 06/01/09 PH 8-7 Bitsy Griffin
- 4. Raising Products to Powers For any nonzero number a and b and any integer n, (ab) n =a n b n (5y) 3 =5 3 y 3 125y 3 06/01/09 PH 8-7 Bitsy Griffin
- 5. Raising Products to Powers (3x) 4 =3 4 x 4 =?? 81x 4 (7c) 2 =?? 49c 2 (15z) 3 =?? 3375z 3 06/01/09 PH 8-7 Bitsy Griffin
- 6. Raising Products to Powers (2x 2 ) 4 =?? 2 4 (x 2 ) 4 =?? 16x 8 (4g 5 ) 2 =?? 4 2 (g 5 ) 2 =?? 16g 10 06/01/09 PH 8-7 Bitsy Griffin
- 7. Raising Products to Powers (x -2 ) 2 (3xy 2 ) 4 =?? x -4 3 4 x 4 (y 2 ) 4 =?? 3 4 x -4 x 4 y 8 =?? 81 x 0 y 8 =?? 81y 8 06/01/09 PH 8-7 Bitsy Griffin
- 8. Raising Products to Powers (6mn) 3 (5m -3 ) 4 =?? 6 3 m 3 n 3 5 4 (m -3 ) 4 =?? 6 3 ● 5 4 m 3 m -12 n 3 =?? 6 3 ● 5 4 m 3 -12 n 3 =?? (135,000 n 3 )/ m 9 06/01/09 PH 8-7 Bitsy Griffin
- 9. Raising Products to Powers All objects, even resting ones, contain energy. The expression 10 -3 (3x10 8 ) 2 describes the amount of resting energy a raisin contains, where 10 -3 kg is the mass of the raisin. Simplify the expression. 06/01/09 PH 8-7 Bitsy Griffin
- 10. Real World Examples Use your calculator to help you. Remember that you may have to convert from standard to scientific notation. 10 -3 (3x10 8 ) 2 9x10 13 06/01/09 PH 8-7 Bitsy Griffin