Integer Power Calculator
Calculate a base raised to an integer exponent
Calculate Power Reset
Power Rules
a^n = a x a x ... x a
Positive exponents repeat multiplication. Zero exponents give 1 for nonzero bases. Negative exponents create reciprocals.
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Note: A zero base with a negative exponent is undefined because it creates division by zero. Very large powers may be shown in scientific notation.
How Integer Powers Work
An integer exponent tells how many times to use a base as a factor. Positive, zero, and negative exponents follow different but related rules.
Positive Exponents
When n is positive, a^n means a multiplied by itself n times.
Zero Exponent
For any nonzero base a, a^0 equals 1.
Negative Exponents
When n is negative, a^n becomes a reciprocal: a^-n = 1/a^n.
Sign Behavior
Negative bases keep a negative result for odd exponents and a positive result for even exponents.
Example: 3^4 = 3 x 3 x 3 x 3 = 81. Also, 2^-3 = 1 / 2^3 = 1/8 = 0.125.
Applications of Integer Powers
Exponent Rules
Scientific Notation
Growth Models
Algebra Simplifying
Compound Growth
Computer Math
Frequently Asked Questions
What is an integer power?▼
An integer power a^n means multiplying the base a by itself n times when n is positive.
What does a negative exponent mean?▼
A negative exponent means reciprocal power: a^-n = 1/a^n, when a is not zero.
What is any number to the power of zero?▼
Any nonzero number raised to the zero power equals 1.
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