 # Exponents - What Is The Relationship Of A Exponent To its Base?

## What Is The Base Of A Number Raised To An Exponent?

Lets start of talking about the rules of exponents which is a multiplication shortcut. Let's start with an example. The expression 34 means 3 is multiplied by itself 4 times: 3 x 3 x 3 x 3 = 9 x 9 = 81. Now let's break this example down into more detail.
• The first thing we notice is this is shorthand for multiplication.
• The expression 34 is read as "three to the fourth power".
• 34 is called the Base - the number being multiplied.
• 34 is called the Exponent - the numbers of time the multiplication is being performed.
• Also 34 equals 81. Since the 81 is the result of multiplying three - four times, it is called a power of four.
• Any Natural Numbers can be a exponent.
• Any base number with an exponent of one, is the base number itself. For example: 61 equals 6.
• Any base number with an exponent of zero, is zero. For example: 90 equals 0. There is one important exception: zero. Example 00 is undefined - not zero!

Exponents Examples

## Math Expression

2 3 23 8
-2.5 3 -2.53 -15.625
2 64 264 18,446,744,073,709,600,000
73 37 7337 8.76891427553567E+68

Exponents Calculator
Instructions Field Name User Input
Practice Exponent instructions:
• If you want to check the answer to a homework problem fill in the empty fields: Base and Exponent.
• If you want to practice solving power and exponent problems, press the New Problem button and it will fill in the Base and Exponent. 