Algebra I in Simple English/Introduction to Basic Algebra Ideas/Exponents and Powers

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Back to Table of Contents OLPC - Algebra 1 in Simple English

(Note to contributors: Please use the ^ symbol to designate exponents when you enter them in the wikibook. I will format them on the student-user interface.--HSTutorials 00:42, 17 July 2006 (UTC)

Vocabulary

Exponent is a number in written in superscript that denotes how many times the base will be multiplied by itself.
Base is the number to be multiplied by itself.
Example:
52=25

Lesson

We use exponents to show when we're multiplying the same number more than one time.

3*3 = 3^2
Three times three equals three to the second power (or three squared)
3*3*3 = 3^3
Three times three times three equals three to the third power (or three cubed)
3*3*3*3= 3^4
Three times three times three times three equal three to the fourth power
2*2*2 = 2^3
Two times two times two equals two to the third power

Note that any number raised to the 0 power is always equal to 1.

2^0 = 1
Two to the zero power equals one

We can also raise any number to a negative exponent. This is called the inverse exponent and places the number on the bottom of a fraction with a 1 on top:

2^-2 = 1/(2^2) = 1/4
Two to the negative two equals one over two to the second power

Example Problems

Let's evaluate these expressions.

7^2

Seven to the second power, or seven squared, means seven times seven.

7*7

Seven times seven is forty-nine.

49

So, seven to the second power equals forty-nine.



Area of a square = (length of the side) ^2

The area, or space inside, of a square is equal to the length of the side of the square to the second power.

Area of a square with side length 3 meters

If the square had a side length of 3 meters,

(3 meters)^2

Then the area would be (3 meters) squared.

3*3 meters^2

3 squared is the same as 3 times 3.

9 square meters

So, the area of a square with a side length of 3 meters is 9 square meters.

c^2 where c=6

First, we replace the variable "c" in the expression with 6, which is what it equals.

6^2

6 squared equals 6 times 6.

6*6

6 times 6 equals 36.

36

So, c squared is 36.

x^3 where x = 10.

First, we replace the variable "x" in the expression with 10, which is what it equals.

10^3

10 to the third power, or 10 cubed, is equal to 10 times 10 times 10.

10*10*10

10 times 10 equals 100.

100*10

100 times 10 equals 1000.

1000

So, x to the third power is 1000.

y^4 where y = 2

First, we replace the variable "y" in the expression with 2, which is what it equals.

2^4

2 to the fourth power is equal to 2 times 2 times 2 times 2.

2*2*2*2

2 times 2 equals 4.

4*2*2

4 times 2 equals 8.

8*2

And 8 times 2 equals 16.

16

So, y to the fourth is 16.

3^-3

Three to the negative third power, which can be expressed as 1 over three cubed.

1/(3^3)

Three cubed equals 3 times 3 times 3 which equals 27.

1/27

So, three to the negative third power equals one twenty-seventh.

Practice Games

http://www.math.com/school/subject2/practice/S2U2L2/S2U2L2Pract.html

http://www.quia.com/pop/50485.html (scientific notation)

http://www.softschools.com/math/games/exponents_practice.jsp

http://www.quia.com/quiz/358716.html (King Kong Scientific Notation)

Practice Problems

(Note: put answer in parentheses after each problem you write)

Evaluate the following expressions:

  1. 6^2 (36)
  2. 2^3 (8)
  3. 4^2 (16)
  4. 5^3 (125)
  5. 2^4 (16)
  6. 9^2 (81)
  7. 8^2 (64)
  8. 5^-3 (1/125)
  9. 6^0 (1)
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