Algebra 1 Common Core Student Edition, Grade 8-9

Co n cep t Byt e Multiplying

Use W ith Lesson 7 -2

Po w er s

You can use patterns to find a shortcut for multiplying powers.

Activity 1

Copy and complete each statement in Exercises 1-8.

1. 22 • 22 = 2 • 2 • 2 • 2 = 24 = 2 2+B

2. 32


3. 33


4. 43


5. 51

6. 63

7. 7 2

3 • 3 • 3 • 3 = 3‘— o 4 — o 2 + B

y = 3. 3. 3. 3. 3 = 3'_ oB _ oB+l

42 = 4 • 4 • 4. 4 • 4 = 4 ^ = 4‘

52 = 5 • 5 • 5 = 5a = 5B+S

63 = B = 6b = 6b +b

76 = jfj = 7 ® = 7 M+B

Co m m o n Co r e St at e St an d ar d s

Pr ep ar es f o r N- RN.A.1 Explain ho w the d e fin ition

o f th e meaning o f rational exponents fo llo w s from

extending the properties of integer exponents to those

values...

MP 7

8. 103 • 107 10 * = 10

9. a. Look fo r a Pattern What pattern do you see in your answers to Exercises 1-8?
   b. Predict Use your pattern to predict the solution to 7 5 • 7s = 7*.
   c. Generalize Use your pattern to predict the value of xn • xm.

You can find a similar pattern when multiplying powers with negative exponents.

Activity 2

Copy and complete each statement in Exercises 10-15.

10. 22 • 2_1 = 2 • 2 • I = 21 = 2 2+®

11. 24 • 2_2 = 2 • 2 • 2 • 2 I.I = 2 " = 2 4+"

12. 33 • 3~ 2 = 3 • 3 • 3 • | | = 3- = 33+s


13. 4~3. 43 = 1. I. I. 4. 4. 4 = 4 = 4


14. 8-4 • 86 = = 8 B = S®*4""


15. 12- 3 • 127 = = 12® = I 2 a+®


16. a. Lo o k f o r a Pat t er n What pattern do you see in your answers to Exercises 10-15?
    b. Predict Use your pattern to predict the solution to 9 5 • 9 -7 = 9B.
    c. Gen er al i ze Use your pattern to predict the value of xn • x~m.

424 Concept Byte Multiplying Powers