The exponent calculator computes any base raised to any power, including negative exponents, fractional exponents (roots), and large powers. Shows result in both decimal and scientific notation.
Exponent Calculator (bⁿ)
How to Use the Exponent Calculator
Exponentiation raises a base to a power: bⁿ = b multiplied by itself n times. The calculator handles all types of exponents.
Negative Exponents
b⁻ⁿ = 1/bⁿ. So 2⁻³ = 1/2³ = 1/8 = 0.125. 10⁻⁶ = 0.000001 (one millionth, the micro- prefix). Negative exponents appear in scientific notation for very small numbers: 1.602 × 10⁻¹⁹ C (elementary charge).
Fractional Exponents (Roots)
b^(1/2) = √b. b^(1/3) = ∛b. 27^(1/3) = 3. 16^(0.25) = 16^(1/4) = 2. For b^(m/n): take the nth root first, then raise to the m power. 8^(2/3) = (∛8)² = 2² = 4.
Financial Application
Compound interest: A = P × (1+r)ⁿ. Invest $1000 at 5% for 10 years: A = 1000 × (1.05)¹⁰. (1.05)¹⁰ ≈ 1.6289. A = $1628.90. The exponent 10 represents 10 years of compounding.
FAQ
What is an exponent?
An exponent tells you how many times to multiply the base by itself. 2⁵ = 2×2×2×2×2 = 32. The base is 2, the exponent is 5. b⁰ = 1 for any b≠0. b¹ = b. Negative exponent: b⁻ⁿ = 1/bⁿ. 2⁻³ = 1/8 = 0.125.
What is a fractional exponent?
b^(1/n) = ∛ⁿb (nth root). 8^(1/3) = ∛8 = 2. 16^(1/2) = √16 = 4. 27^(2/3) = (27^(1/3))² = 3² = 9. In general, b^(m/n) = (b^(1/n))^m = nth root of b, raised to the mth power.
Is this calculator free?
Yes, completely free with no signup required. All calculations run in your browser.
Is my data private?
Yes. All calculations run locally. Nothing is transmitted.
How do you calculate large exponents?
For large integer exponents, use logarithms: bⁿ = e^(n×ln(b)). 2¹⁰⁰ = e^(100×ln(2)) = e^(69.32) ≈ 1.267 × 10³⁰. Very large exponents quickly produce numbers with hundreds or thousands of digits. The calculator handles up to 15 significant figures.