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Exponents - What Is The Relationship Of A Exponent To its Base?
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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 3
^{4}
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 3
^{4}
is read as "three to the fourth power".
3
^{4}
is called the
Base
- the number being multiplied.
3
^{4}
is called the
Exponent
- the numbers of time the multiplication is being performed.
Also 3
^{4}
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: 6
^{1}
equals 6.
Any base number with an exponent of zero, is zero. For example: 9
^{0}
equals 0. There is one important exception: zero. Example 0
^{0}
is
undefined
- not zero!
Exponents Examples
Input Base
Input Exponent
Math Expression
Your Answer
2
3
2
^{3}
8
-2.5
3
-2.5
^{3}
-15.625
2
64
2
^{64}
18,446,744,073,709,600,000
73
37
73
^{37}
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
.
Next fill in the
Your Answer
field with your answer to the problem.
Press the
Submit
button to see if your answer is correct.
Base
You can enter up to 6 digits
Exponent
You can enter up to 6 digits
Your Answer
You can enter up to 10 digits (input integer or decimal)
Correct Answer
See More About Roots Of Numbers