Exponent Calculator
Calculate any base raised to any exponent with our free exponentiation calculator. Get instant results, expanded step-by-step form, and interactive growth chart online.
About This Calculator
The Exponent Calculator computes any base raised to any exponent (power), also known as exponentiation. Enter a base number and an exponent to get the result, a step-by-step expanded form showing the multiplication, and an interactive growth chart that visualizes how the base grows as the exponent increases. This tool supports positive exponents, negative exponents (which produce reciprocals), fractional exponents (which combine powers and roots), and the special case of zero exponents (any non-zero base raised to 0 equals 1).
Exponentiation follows the formula: result = baseexponent. For integer exponents, the expanded form shows repeated multiplication. For fractional exponents, the calculator shows the power-and-root combination. The growth chart plots the result at each integer step up to the given exponent (or up to 20 for large exponents), helping you understand the exponential relationship visually.
Laws of exponents used in this calculator include: aᵐ x aⁿ = a^(m+n), a⁻ⁿ = 1/aⁿ, a^0 = 1 (for a ≠ 0), a^(m/n) = (ⁿsqrta)ᵐ, and (aᵐ)ⁿ = a^(mn). These rules are fundamental across algebra, calculus, physics, engineering, and computer science.
Frequently Asked Questions
What is an exponent?
An exponent (or power) indicates how many times to multiply the base by itself. For example, 2^3 means 2 x 2 x 2 = 8. The exponent is written as a superscript number after the base.
What does a negative exponent mean?
A negative exponent means the reciprocal of the base raised to the positive exponent. For example, 2⁻^3 = 1 / (2 x 2 x 2) = 1/8 = 0.125. A negative exponent never produces a negative result; it simply gives the reciprocal.
What is any number raised to the power of zero?
Any non-zero number raised to the power of zero equals 1. For example, 5^0 = 1 and 1000^0 = 1. The only exception is 0^0, which is undefined in standard mathematics.
How do fractional exponents work?
A fractional exponent combines a power and a root. For example, 4^1/2 (4 raised to the power of 1/2) equals the square root of 4, which is 2. More generally, a^(m/n) = (ⁿsqrta)ᵐ, meaning the n-th root of a raised to the power m.
What is the difference between an exponent and a power?
The terms are often used interchangeably, but strictly speaking: the exponent is the superscript number (e.g., the 3 in 2^3), while the power is the entire expression (2^3) or the result (8). So 2^3 reads as "2 to the power of 3" where 2 is the base and 3 is the exponent.
How do you multiply numbers with the same base but different exponents?
When multiplying numbers with the same base, add the exponents: aᵐ x aⁿ = a^(m+n). For example, 2^3 x 2^2 = 2^(3+2) = 2^5 = 32. This is one of the fundamental laws of exponents taught in algebra.
What is the largest exponent this calculator supports?
The calculator handles any real exponent value. For very large exponents the result may display in scientific notation, and the growth chart shows up to 20 steps. The expanded form limits the display to 20 terms for readability. Extremely large values (exceeding Number.MAX_VALUE) will show as Infinity.