Digits, Grade 8, Volume 2, Homework Helper

### 15-4: Exponents and Division

#### Part 1

Intro

Exponents allow you to write expressions containing repeated multiplication more efficiently and precisely.

Simplify the expression fraction 7 to the eighth , over 7 cubed end fraction . .

table with 3 rows and 2 columns , row1 column 1 , fraction 7 to the eighth , over 7 cubed end fraction . , column 2 equals . fraction cross out enclosing , 7 , end crossout middle dot , to the first , cross out enclosing , 7 , end crossout middle dot , to the first , cross out enclosing , 7 , end crossout middle dot 7 middle dot 7 middle dot 7 middle dot 7 middle dot 7 , over , sub 1 , cross out enclosing , 7 , end crossout middle dot , sub 1 , cross out enclosing , 7 , end crossout middle dot , sub 1 , cross out enclosing , 7 , end crossout end fraction , column 2 equals . fraction 7 middle dot 7 middle dot 7 middle dot 7 middle dot 7 , over 1 end fraction , column 2 equals , 7 to the fifth , end table

Dividing Powers with the Same Base

Arithmetic: fraction 7 to the eighth , over 7 cubed end fraction . equals . 7 super 8 minus 3 end super . equals , 7 to the fifth

Algebra: fraction a to the m , over a to the n end fraction . equals . a super m minus n end super . comma w h e r e a not equal to 0 and m and n are , integers and m and n are integers

Example Simplifying Quotients of Powers

Use the numbers below to simplify each expression.

20   9   7   3   4   10   13

• a.

• b.

• c.

Solution

• a.

• b. table with 2 rows and 1 column , row1 column 1 , fraction y to the thirteenth , over y to the ninth end fraction . equals . y super 13 minus 9 end super , row2 column 1 , equals , y to the fourth , end table

• c. table with 2 rows and 1 column , row1 column 1 , fraction d to the twentieth , over d to the thirteenth end fraction . equals . d super 20 minus 13 end super , row2 column 1 , equals , d to the seventh , end table

End ofPage 517