Basic Algebra/Introduction to Basic Algebra Ideas/Exponents and Powers
- a number written in superscript that denotes how many times the base will be multiplied by itself.
- Base (or radix)
- the number to be multiplied by itself.
In this example, the base is 5 and the exponent is 2.
We use exponents to show when we're multiplying the same number more than one time.
- Three times three equals three to the second power (or three squared)
- Three times three times three equals three to the third power (or three cubed)
- Three times three times three times three equal three to the fourth power
- Two times two times two equals two to the third power
Note that any nonzero number raised to the 0 power is always equal to 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:
- Two to the negative two equals one over two to the second power
Let's evaluate these expressions.
- Example 1
- Seven to the second power, or seven squared, means seven times seven.
- Seven times seven is forty-nine.
- Seven to the second power equals forty-nine.
- Example 2
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,
- Then the area would be (3 meters) squared.
- 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.
- Example 3
- First, we replace the variable "c" in the expression with 6, which is what it equals.
- 6 squared equals 6 times 6.
- 6 times 6 equals 36.
- So, c squared is 36.
- Example 4
where x = 10.
- First, we replace the variable "x" in the expression with 10, which is what it equals.
- 10 to the third power, or 10 cubed, is equal to 10 times 10 times 10.
- 10 times 10 equals 100.
- 100 times 10 equals 1000.
- So, x to the third power is 1000.
- Example 5
where y = 2
- First, we replace the variable "y" in the expression with 2, which is what it equals.
- 2 to the fourth power is equal to 2 times 2 times 2 times 2.
- 2 times 2 equals 4.
- 4 times 2 equals 8.
- And 8 times 2 equals 16.
- So, y to the fourth is 16.
- Example 6
- Three to the negative third power, which can be expressed as 1 over three cubed.
- Three cubed equals 3 times 3 times 3 which equals 27.
- So, three to the negative third power equals one twenty-seventh.
- http://www.quia.com/pop/50485.html (scientific notation)
- http://www.quia.com/quiz/358716.html (King Kong Scientific Notation)
- http://www.shodor.org/interactivate/activities/OrderOfOperationsFou/ (order of operations including exponents)
Evaluate the following expressions: