This document discusses how to simplify powers of monomials. It provides two rules: 1) To raise a power to a power, multiply the exponents and keep the same base. For example, (bm)n = bmn. 2) To find the power of a product, raise each factor to that power. For example, abm= ambm. It also notes that expressions like (2x)3 and 2x3 are not the same - the first involves multiplying 2x by itself 3 times while the second involves raising 2 to the power of 3 and x to the power of 3 separately. Students are directed to practice problems on page 205.

1. 6.2 Powers of MonomialsObjective: To simplify a power of a power and a power of a productFrameworks: 10.P.1, 10.P.7

2. What is 334?334= (3*3*3)*(3*3*3)*(3 *3* 3)*(3*3*3) = 312What is the pattern?

3. Multiplying MonomialsTo raise a power to a power, you multiply the exponents and keep the same base.

4. Power of a PowerFor all real numbers b and all positive integers m and n, (bm)n = bmn

5. Try some:(c7)5(y3)10(x3)3(a21)2

6. What about (2x)3 ?(2x)3 = 2x * 2x * 2x = (2 * 2 * 2) * (x * x * x) = 23 * x3 = 8x3To find the power of a product, raise each factor to that power.

7. Power of a ProductFor all real numbers a and b and all positive integers, abm= ambm

8. Notice:Do not confuse (2x)3 and 2x3(2x)3 means 2x * 2x * 2x2x3 means 2 * x * x * x

9. Try some: (-4c)3(-xy2)4-4x(5x3)2(-2a4b6)5

10. Turn to page 205Do 1-16