1. Multiplying and Dividing Monomials

2. Rules for Multiplication  When you multiply monomials and their bases are the same, you keep the base and add the exponents.  Example: z 4 · z 2 = z 4+2 = z 6  Example: 5 2 · 5 9 = 5 2+9 = 5 11

3. Independent Practice  A. n 3 · n 2  B. f 6 · f 3  C. 8 · 8 5 Answers: A.n 5 B.f 9 C.8 6

4. Rules for Division  When you divide monomials and their bases are the same, you keep the base and subtract the exponents.  Example: b 10 ÷ b 3 = b 10-3 = b 7  Example: 6 5 ÷ 6 = 6 5-1 = 6 4

5. Independent Practice  A. w 12 ÷ w 5  B. p 6 ÷ p 4  C. 9 7 ÷ 9 2 Answers: A.w 7 B.p 2 C.9 5

6. Sample ARMT Questions  Simplify.  6 10 ÷ (6 7 ÷ 6 2 )  Following the order of operations, we would take care of the parenthesis first. Since both bases are 6, we keep the base and subtract (because we are dividing). 7-2 = 5. Then we have 6 10 divided by 6 5. We have the same base so we keep it and subtract. 10 - 5 = 5. Our answer is 6 5.

7. Sample ARMT Questions Cont. 35 · 38 · 3235 · 38 · 3235 · 38 · 3235 · 38 · 32 3 · 3 3 3 · 3 3 Simplify the top, simplify the bottom, and then divide. Since the bases are the same throughout the whole problem, we know that the base of our answer will be 3. The top gives us 3 5+8+2 = 3 15 The bottom gives us 3 1+3 = 3 4 Last we divide. We keep the base of 3 and subtract the exponents. 15 – 4 = 11. Our answer is 3 11.

8. Sample ARMT Questions Cont.  Shelly drew a square and marked the lengths of the sides using exponential notation. She then wrote the expression 4 5 x 4 5 to represent the area of the square.  What is equivalent to the area, in square units, of Shelly’s square?

9. Sample ARMT Questions Cont. 4545 4545 To find the area of the square, just multiply the length times the width. 4 5 x 4 5 = 4 5+5 = 4 10

10. Conclusion  When dealing with monomials, remember to be MADS about monomials.  When you Multiply, you Add the exponents.  When you Divide, you Subtract the exponents.