Basic Algebra/Introduction to Basic Algebra Ideas/Exponents and Powers
Jump to navigation
Jump to search
Vocabulary[edit  edit source]
 Exponent
 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.
Example:
In this example, the base is 5 and the exponent is 2.
Lesson[edit  edit source]
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
Example Problems[edit  edit source]
Let's evaluate these expressions.




 Seven to the second power equals fortynine.
 What is the area of a square with a side of 3 meters length?








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






 So, c squared is 36.
 where .








 So, x to the third power is 1000.
 where










 So, y to the fourth is 16.




 So, three to the negative third power equals one twentyseventh.
Practice Games[edit  edit source]
 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)
 http://www.shodor.org/interactivate/activities/OrderOfOperationsFou/ (order of operations including exponents)
Practice Problems[edit  edit source]
Use /
as the fraction line!