Exponent Calculator
Enter the base and exponent to calculate the result below.
ax = ?
Results:
How to Calculate an Exponent
An exponent is the number of times the base value should be multiplied by itself. To calculate a number raised to an exponent, multiply the number by itself for each value of the exponent.
So 52 is the same as 5 × 5 and 53 is the same as 5 × 5 × 5.
Calculating an exponent is also sometimes referred to as raising a number to the nth power.
For example, calculate the result of 84.
84 = 8 × 8 × 8 × 8
84 = 4,096
Thus, 84, or 8 to the 4th power, is equal to 8 times 8 times 8 times 8, which is equal to 4,096.
How to Calculate a Negative Exponent
What do you do if the exponent is negative? For a negative exponent rather than multiplying the number by itself the number of times for the exponent, you divide the number by itself, starting with 1.
So 5-2 is the same as 1 ÷ 5 ÷ 5 and 5-3 is the same as 1 ÷5 ÷ 5 ÷ 5.
Negative exponents are often expressed as 1 over the base with a positive exponent.
5-2 = 152
For example, calculate the result of 84.
8-4 = 184
8-4 = 18 × 8 × 8 × 8
8-4 = 14,096
8-4 = 0.000244140625
Thus, 8-4 is equal to 0.000244140625.
Special Exponent Rules
There are some special rules with exponents that are important to remember.
When the exponent is 1, the result of raising a base to the exponent will always be equal to the base.
a1 = a
When the exponent is 0, the result of raising a base to the exponent will always be equal to 1.
a0 = 1
When the exponent is 2 you can also say that the base value is squared. When the exponent is 3 you can say that the base value is cubed.
The calculator above will handle these special cases along with negative exponents to solve the answer.
