Nth Power Calculator
Calculate any base raised to the power of n (x^n) for positive, negative, and fractional exponents with step-by-step exponent laws.
Did this calculation save you time?
Student ProjectHi! I'm a student developer building Calculat in my spare time. I was tired of searching for basic math tools and having to click through 10 spammy popups, loan ads, and cookie trackers.
I keep this website 100% free, private, and ad-free. If this helped you with your homework, project, or finances today, bookmarking this page or telling a friend helps me keep building more free tools!
What Is a Nth Power Calculator?
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.
How to Use This Calculator
- Enter the base number (b) and the exponent (n).
- View the calculated power result in standard and scientific notation.
- Follow the step-by-step explanation applying laws of exponents.
Laws of Exponents
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.
Worked Example
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
Tips & Key Notes
- Negative exponent rule: b^(-n) = 1 / (b^n). For example, 2^(-3) = 1 / 8 = 0.125.
- Fractional exponent rule: b^(1/n) = ⁿ√b. For example, 9^(1/2) = √9 = 3.
- Power of zero rule: Any non-zero number raised to the 0 power equals 1.
Frequently Asked Questions
What is 0 to the power of 0?
In algebra and combinatorics, 0⁰ is commonly defined as 1, while in mathematical analysis it is considered an indeterminate form.
How do negative exponents work?
A negative exponent indicates reciprocal division: x^(-n) = 1 / (x^n). For instance, 10^(-2) = 1 / 100 = 0.01.
What is a fractional exponent?
A fractional exponent represents a radical root: x^(m/n) = ⁿ√(x^m). For example, 8^(2/3) = (∛8)² = 2² = 4.
What happens when you multiply powers with the same base?
Add the exponents together: b^m × b^n = b^(m + n).
Related Calculators
Explore similar toolsSquare Calculator (x²)
Calculate the square of any positive or negative number (x² = x × x) with scientific notation and step-by-step arithmetic.
Cube Calculator (x³)
Calculate the cube of any positive or negative number (x³ = x × x × x) with scientific notation and step-by-step arithmetic.
Nth Root Calculator
Calculate the nth root of any number (ⁿ√x). Supports even and odd roots, real roots, radical expressions, and step-by-step solutions.