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Homework: Extending the Idea of Exponents

Module by: Kenny M. Felder. E-mail the author

Summary: This module provides practice problems designed to develop concepts related to exponents.

Answer the following questions.

Exercise 1

50 5 0

Exercise 2

5−2 5 2

Exercise 3

= −2−2 = 2 2

Exercise 4

= −2−3 = 2 3

Exercise 5

= 6−3 = 6 3

Exercise 6

x0= x 0 =

Exercise 7

(x−a) = x a =

In those last two problems, of course, you have created the general rules for zero and negative exponents. So hey, what happens to our trusty rules of exponents? Let’s try…

Exercise 8

Let’s look at the problem 60⁢6x 6 0 6 x two different ways.

  • a. What is 60 6 0 ? Based on that, what is 60⁢6x 6 0 6 x ?
  • b. What do our rules of exponents tell us about 60⁢6x 6 0 6 x ?

Exercise 9

Let’s look at the problem 606x606x size 12{ { {6 rSup { size 8{0} } } over {6 rSup { size 8{x} } } } } {} two different ways.

  • a. What is 60 6 0 ? Based on that, what is 606x606x size 12{ { {6 rSup { size 8{0} } } over {6 rSup { size 8{x} } } } } {}?
  • b. What do our rules of exponents tell us about 606x606x size 12{ { {6 rSup { size 8{0} } } over {6 rSup { size 8{x} } } } } {}?

Exercise 10

Let’s look at the problem 6−4⁢63 6 4 6 3 two different ways.

  • a. What does 6−4 6 4 mean? Based on that, what is 6−4⁢63 6 4 6 3 ?
  • b. What do our rules of exponents tell us about 6−4⁢63 6 4 6 3 ?

Exercise 11

What would you square if you wanted to get x36 x 36 ?

Simplify:

Exercise 12

1 x − 5 1 x − 5 size 12{ { {1} over {x rSup { size 8{ - 5} } } } } {}

Exercise 13

8x 3 y 7 12 x − 3 y 4 8x 3 y 7 12 x − 3 y 4 size 12{ { {8x rSup { size 8{3} } y rSup { size 8{7} } } over {"12"x rSup { size 8{ - 3} } y rSup { size 8{4} } } } } {}

Now let’s solve a few equations.

Exercise 14

Solve for x x: 3x+2=38−x 3 x 2 3 8 x . (Hint: If the bases are the same, the exponents must be the same!)

Exercise 15

Solve for x x: 2 4x- 3 = 8 x - 2 2 4x- 3 = 8 x - 2 .

Hint:

Start by rewriting 8 as 23, then use the rules of exponents.

Exercise 16

Solve for x x: 5(3x2+13x+10)= 25x+2 5(3x2+13x+10) size 12{5 rSup { size 8{ \( 3x rSup { size 6{2} } +"13"x+"10" \) } } } {}= 25 x 2 . (*No more hints this time, you’re on your own.)

Exercise 17

Solve for x x: 7x⁢7x+2=1 7 x 7 x 2 1

Exercise 18

Solve for x x: 7xx+2=1 7 x x 2 1

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