Digits, Grade 8, Volume 2, Homework Helper

### 15-3: Exponents and Multiplication

#### Part 1

Intro

Remember that exponents are a shorthand notation that allows you to write expressions containing repeated multiplication more efficiently and precisely. Multiplying Powers with the Same Base To multiply powers with the same base, add the exponents.

Arithmetic: 7 squared , middle dot , 7 cubed , equals . 7 super 2 plus 3 end super . equals , 7 to the fifth

Algebra: a to the m , middle dot , a to the n , equals . a super m plus n end super . comma where a≠0 and m and n are integers

Example Simplifying Products of Powers

Use the numbers to simplify each expression.

8   18   12   3   5   2   10

• a. • b. • c. Solution

• a. table with 2 rows and 4 columns , row1 column 1 , 5 squared , middle dot , 5 to the eighth , column 2 , column 3 equals , column 4 5 super 2 plus 8 end super , column 2 , column 3 equals , column 4 5 to the tenth , end table

• b. table with 2 rows and 4 columns , row1 column 1 , x cubed , middle dot , x to the fifth , middle dot , x to the tenth , column 2 , column 3 equals , column 4 x super 3 plus 5 plus 10 end super , column 2 , column 3 equals , column 4 x to the eighteenth , end table

• c. Remember to multiply the coefficients of m just as you would multiply two numerical expressions. Only the exponents get added.

table with 3 rows and 4 columns , row1 column 1 , 2 , m to the tenth , middle dot 5 m , column 2 , column 3 equals , column 4 open . 2 middle dot 5 . close . middle dot . open . m to the tenth , middle dot , m squared . close , column 2 , column 3 equals , column 4 open . 2 middle dot 5 . close . middle dot . m super 10 plus 2 end super , column 2 , column 3 equals , column 4 10 , m to the twelfth , end table

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