Exponents and Powers

Don't be afraid when you see something like 32.  Numbers like the 2 shown are called exponents, and they have a special meaning in math.  The number 3 is called the base, and the entire expression, 32 is a power.

Important Vocabulary

Before progressing any further, lets learn some important terminology. View the picture below to know what is being referred to.

exponent vocabulary


What Does a "Power" Mean in Mathematics?

A power is a multiplication problem.  Mathematicians are lazy, so sometimes they make shortcuts for writing problems faster. 


Whatever the base is (bigger number) that is the number that is going to get multiplied.  The exponent (smaller number) is the number of times you will multiply the base times itself

Picture explanation

explaining exponents




More Examples: Follow the Pattern if it Helps You

◊  23 = 2·2·2  ◊  44 = 4·4·4·4  ◊  52 = 5·5  ◊  85 = 8·8·8·8·8 

 Sometimes, powers are evaluated like so:  33 = 3·3·3 = 9·3 = 27

They can also apply to variables: 

x3 = x·x·x      or     x5 = x·x·x·x·x     or     y4 = y·y·y·y

Special Lingo for Powers

  • "squared" means you have a power of 2

  • "cubed" means you have a power of 3


  • "five squared" is the power 52

  • "six cubed" is the power 63


What is the Value of 40, 100, or even x0?  

Listen carefully:  Any power where the "raised number" is 0 is equal to 1.

I know this sounds strange, but believe us it is true.  It always equals 1!

Examples:  30 = 1   ◊   90 = 1      x0 = 1   ◊   (any number)0 = 1

So, now that you know about exponents, why not learn about subscripts?  Take a look at our page on calculating slope to learn why 32 isn't 32!

Other pre-algebra topics or the GradeA homepage.



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