Calculate any base raised to the power of n (x^n) for positive, negative, and fractional exponents with step-by-step exponent laws.
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Exponentiation is a mathematical operation written as b^n, involving two numbers: the base b and the exponent or power n. When n is a positive integer, it represents repeated multiplication.
b^n = \underbrace{b \times b \times \dots \times b}_{n \text{ times}}, \quad b^{-n} = \frac{1}{b^n}, \quad b^0 = 1 \quad (b \neq 0)Negative exponents invert the base. Any non-zero base raised to the zero power equals 1.
Scenario: Calculate 2 raised to the power of 10
Base: b = 2, Exponent: n = 10
Operation: 2¹⁰ = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
Result: 1,024
In algebra and combinatorics, 0⁰ is commonly defined as 1, while in mathematical analysis it is considered an indeterminate form.
A negative exponent indicates reciprocal division: x^(-n) = 1 / (x^n). For instance, 10^(-2) = 1 / 100 = 0.01.
A fractional exponent represents a radical root: x^(m/n) = ⁿ√(x^m). For example, 8^(2/3) = (∛8)² = 2² = 4.
Add the exponents together: b^m × b^n = b^(m + n).
Calculate the square of any positive or negative number (x² = x × x) with scientific notation and step-by-step arithmetic.
Calculate the cube of any positive or negative number (x³ = x × x × x) with scientific notation and step-by-step arithmetic.
Calculate the nth root of any number (ⁿ√x). Supports even and odd roots, real roots, radical expressions, and step-by-step solutions.