Exponent Calculator — Calculate x^y Powers
Calculate any base raised to any exponent (x^y). Shows step-by-step solution for small integers and includes a complete exponent rules reference.
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Scientific Notation
Step-by-Step Expansion
Laws of Exponents
Product Rule
x^m · x^n = x^(m+n)
2^3 · 2^4 = 2^7 = 128
Quotient Rule
x^m / x^n = x^(m-n)
5^6 / 5^2 = 5^4 = 625
Power Rule
(x^m)^n = x^(m×n)
(3^2)^4 = 3^8 = 6561
Zero Exponent
x^0 = 1 (x ≠ 0)
99^0 = 1
Negative Exponent
x^(-n) = 1/x^n
2^(-3) = 1/8
Fractional Exponent
x^(1/n) = ⁿ√x
8^(1/3) = 2
Frequently Asked Questions
What is an exponent?
An exponent (or power) indicates how many times a base number is multiplied by itself. In x^n, x is the base and n is the exponent. For example, 2^5 = 2 × 2 × 2 × 2 × 2 = 32.
What is x^0?
Any non-zero number raised to the power of 0 equals 1. For example, 5^0 = 1, 100^0 = 1. This is a fundamental rule of exponents. The expression 0^0 is considered indeterminate.
What is a negative exponent?
A negative exponent means the reciprocal: x^(-n) = 1/x^n. For example, 2^(-3) = 1/2^3 = 1/8 = 0.125.
What is a fractional exponent?
A fractional exponent represents a root: x^(1/n) = nth root of x. For example, 8^(1/3) = cube root of 8 = 2. More generally, x^(m/n) = (nth root of x)^m.
What is scientific notation and how does it relate to exponents?
Scientific notation uses powers of 10 to express very large or small numbers. For example, 6.022 × 10^23 (Avogadro's number) or 1.6 × 10^(-19). Exponents make working with these numbers much easier.