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# Algebra 6 Point 2

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### Algebra 6 Point 2

1. 1. 6.2 Powers of Monomials<br />Objective: <br /><ul><li>To simplify a power of a power and a power of a product</li></ul>Frameworks: 10.P.1, 10.P.7<br />
2. 2. What is 334?<br />334= (3*3*3)*(3*3*3)*(3 *3* 3)*(3*3*3) <br />= 312<br />What is the pattern?<br />
3. 3. Multiplying Monomials<br />To raise a power to a power, you multiply the exponents and keep the same base.<br />
4. 4. Power of a Power<br />For all real numbers b and all positive integers m and n, <br />(bm)n = bmn<br />
5. 5. Try some:<br />(c7)5<br />(y3)10<br />(x3)3<br />(a21)2<br />
6. 6. What about (2x)3 ?<br />(2x)3 = 2x * 2x * 2x<br /> = (2 * 2 * 2) * (x * x * x)<br /> = 23 * x3 = 8x3<br />To find the power of a product, raise each factor to that power.<br />
7. 7. Power of a Product<br />For all real numbers a and b and all positive integers, <br />abm= ambm<br />
8. 8. Notice:<br />Do not confuse (2x)3 and 2x3<br />(2x)3 means 2x * 2x * 2x<br />2x3 means 2 * x * x * x<br />
9. 9. Try some: <br />(-4c)3<br />(-xy2)4<br />-4x(5x3)2<br />(-2a4b6)5<br />
10. 10. Turn to page 205<br />Do 1-16<br />