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Sample Test: Exponents

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

Summary: This module provides a sample test over exponents.

Simplify. Your answer should not contain any negative or fractional exponents.

Exercise 1

x6 x 6

Exercise 2

x0 x 0

Exercise 3

x18 x 1 8

Exercise 4

x23 x 2 3

Exercise 5

1 a 3 1 a 3 size 12{ { {1} over {a rSup { size 8{ - 3} } } } } {}

Exercise 6

232 2 3 2

Exercise 7

12x 1 2 x

Exercise 8

22 2 2

Exercise 9

23 2 3

Exercise 10

2-1 2 -1

Exercise 11

912 9 1 2

Exercise 12

812 8 1 2

Exercise 13

y14y34 y 1 4 y 3 4

Exercise 14

4x 4 y 5 z 6 wxy 3 z 3 4x 4 y 5 z 6 wxy 3 z 3 size 12{ { {4x rSup { size 8{4} } y rSup { size 8{5} } z} over {6 ital "wxy" rSup { size 8{ - 3} } z rSup { size 8{3} } } } } {}

Exercise 15

x123 x 1 2 3

Exercise 16

x122 x 1 2 2

Exercise 17

x 6 3 x 6 3 size 12{x rSup { size 8{ { {6} over {3} } } } } {}

Exercise 18

x34 x 3 4

Exercise 19

4×912 4 9 1 2

Exercise 20

412912 4 1 2 9 1 2

Exercise 21

Give an algebraic formula that gives the generalization for #18-19.

Solve for xx:

Exercise 22

8x=64 8 x 64

Exercise 23

8x=8 8 x 8

Exercise 24

8x=1 8 x 1

Exercise 25

8x=2 8 x 2

Exercise 26

8x=18 8 x 1 8

Exercise 27

8x=164 8 x 1 64

Exercise 28

8x=12 8 x 1 2

Exercise 29

8x=0 8 x 0

Exercise 30

Rewrite 1x231x23 size 12{ { {1} over { nroot { size 8{3} } {x rSup { size 8{2} } } } } } {} as xsomething.

Solve for xx:

Exercise 31

2x+32x+4=2 2 x 3 2 x 4 2

Exercise 32

3(x2)3(x2) size 12{3 rSup { size 8{ \( x rSup { size 6{2} } \) } } } {} = 193x193x size 12{ left ( { {1} over {9} } right ) rSup { size 8{3x} } } {}

Exercise 33

A friend of yours is arguing that x⅓x⅓ should be defined to mean something to do with “fractions, or division, or something.” You say “No, it means _____ instead.” He says “That’s a crazy definition!” Give him a convincing argument why it should mean what you said it means.

Exercise 34

On October 1, I place 3 sheets of paper on the ground. Each day thereafter, I count the number of sheets on the ground, and add that many again. (So if there are 5 sheets, I add 5 more.) After I add my last pile on Halloween (October 31), how many sheets are there total?

  • a. Give me the answer as a formula.
  • b. Plug that formula into your calculator to get a number.
  • c. If one sheet of paper is 12501250 size 12{ { {1} over {"250"} } } {} inches thick, how thick is the final pile?

Exercise 35

Depreciation

The Web site www.bankrate.com defines depreciation as “the decline in a car’s value over the course of its useful life” (and also as “something new-car buyers dread”). The site goes on to say:

Let’s start with some basics. Here’s a standard rule of thumb about used cars. A car loses 15 percent to 20 percent of its value each year.

For the purposes of this problem, let’s suppose you buy a new car for exactly $10,000, and it loses only 15% of its value every year.

  • a. How much is your car worth after the first year?
  • b. How much is your car worth after the second year?
  • c. How much is your car worth after the nth year?
  • d. How much is your car worth after ten years? (This helps you understand why new-car buyers dread depreciation.)

Exercise 36

Draw a graph of y=2×3x y 2 3 x . Make sure to include negative and positive values of xx.

Exercise 37

Draw a graph of y=13x3 y 1 3 x 3 . Make sure to include negative and positive values of xx.

Exercise 38

What are the domain and range of the function you graphed in number 36?

Extra Credit:

We know that a+b2 a b 2 is not, in general, the same as a2+b2 a 2 b 2 . But under what circumstances, if any, are they the same?

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