Exponent Calculator
A power uses base^exponent. For whole exponents, it means multiplying the base by itself that many times.
Enter base and power
Enter the base and the exponent exactly as the expression is written. Parentheses matter when the base is negative. (-2)^4 and -2^4 are often interpreted differently by calculators.
Use this page for powers, repeated multiplication, negative exponents and quick exponent checks. If your expression includes several operations, use parentheses to show what belongs to the base.
What the power result means
An exponent tells how a base is used in a power. For positive whole number exponents, it means repeated multiplication. For example, 3^4 means 3 x 3 x 3 x 3.
Negative exponents do not make the result negative by themselves. They create reciprocal powers. For example, 2^-3 equals 1 / 2^3, which is 1/8.
Fractional exponents connect powers and roots. A one half exponent means square root when the value is in the real number domain.
Exponent rule used here
For a positive whole exponent n, a^n means multiply a by itself n times. For a negative exponent, a^-n = 1 / a^n when a is not zero. For exponent zero, a^0 = 1 when a is not zero.
If the base is negative, parentheses decide whether the negative sign is part of the base. That is why calculator input needs care.
Calculating 3 to the 4th
(-2)^4 equals 16 because the base is negative 2, and it is multiplied by itself four times. The negatives pair off. But -2^4 is often read as -(2^4), which equals -16.
For a negative exponent, 5^-2 equals 1 / 25, or 0.04. The exponent changes position, not the sign of the answer.
A quick check is to rewrite the exponent rule in words. Ask whether the power applies to the number alone or to the signed value inside parentheses.
Negative bases and parentheses
The biggest mistake is missing parentheses around a negative base. If the negative sign belongs to the base, put the base in parentheses.
Another mistake is thinking a negative exponent means a negative result. It means reciprocal. The sign of the result depends on the base and exponent.
Also watch zero. Zero can be raised to positive exponents, but negative exponents would require division by zero.
Exponent Calculator FAQ
Why does -2^4 give -16?
Many calculators read -2^4 as -(2^4). The exponent applies to 2 first, then the negative sign is applied. That gives -16.
If you mean negative 2 raised to the fourth power, enter (-2)^4. That gives 16.
This is not the calculator changing the math. It is following the usual order of operations, where exponents are evaluated before the leading minus sign unless parentheses change the grouping.
What does a negative exponent mean?
A negative exponent means reciprocal. For example, 2^-3 equals 1 / 2^3, which is 1/8.
It does not automatically make the answer negative. It changes the power into a fraction.
If the base is negative, handle the sign separately. Parentheses decide whether the negative sign is part of the base.
What is any number to the zero power?
Any non zero number to the zero power is 1. This rule keeps exponent patterns consistent.
Zero to the zero power is a special case and may be treated differently depending on context.
For ordinary calculator work, be careful when a formula creates 0^0. It may signal that the expression needs a domain check instead of a simple numeric shortcut.
Do parentheses change exponent answers?
Yes. Parentheses decide what the exponent applies to. (-3)^2 means negative 3 is the base. -3^2 often means the negative sign is outside the power.
When the base is negative or has more than one term, use parentheses.
Can exponents be decimals?
Yes. Decimal and fractional exponents are possible. They often connect to roots. For example, x^(1/2) means the square root of x.
For school work, make sure your class has covered fractional exponents before using that form.
Decimal exponents can also produce approximate values, so the displayed result may be rounded. If the problem expects exact algebra, fractional exponent form may be clearer.
How can I check an exponent result?
For whole number exponents, expand the power as repeated multiplication. For 4^3, write 4 x 4 x 4 and compare the result.
For negative or fractional exponents, rewrite the expression using reciprocal or root rules. This usually reveals whether the input was grouped correctly.