Exponent Calculator

Calculate Powers (x^y)

x^y = x × x × x... (y times)

Base (x)

Exponent (y)

Calculate Roots (ⁿ√x)

ⁿ√x = x^(1/n)

Number (x)

Root Index (n)

Exponential Function (e^x)

e^x where e ≈ 2.71828

Exponent (x)

Quick Examples

Exponent Rules Reference

Product Rule:
x^a × x^b = x^(a+b)

Quotient Rule:
x^a ÷ x^b = x^(a-b)

Power Rule:
(x^a)^b = x^(a×b)

Zero Exponent:
x⁰ = 1 (x ≠ 0)

Negative Exponent:
x^-a = 1/x^a

Fractional Exponent:
x^(a/b) = ^b√(x^a)

Other Math Calculators

Scientific Calculator Fraction Calculator Percentage Calculator Random Number Generator Percent Error Calculator Binary Calculator Hex Calculator Half-Life Calculator Quadratic Formula Calculator Log Calculator Ratio Calculator Root Calculator LCM Calculator GCF Calculator Factor Calculator Rounding Calculator Matrix Calculator Scientific Notation Calculator Big Number Calculator

Exponent Calculator — quick guide

1) Core idea

Compute powers x^y, n-th roots x^(1/n), and the natural exponential e^x with smart handling for big/small outputs.

2) How this tool works

Powers: uses Math.pow(x, y), with guardrails for 0^0 and non-finite results.
Roots: computes x^(1/n) and signs correctly for odd roots of negatives.
e^x: uses Math.exp(x) and flags overflow when needed.

3) Sanity checks

x^0 = 1 for x ≠ 0; 0^0 is undefined here.
Even root of a negative → complex (not shown); odd roots stay real.
e^0 = 1, e^1 = e ≈ 2.71828.

4) Shortcuts that help

x^(a/b) = ᵇ√(x^a) when real-valued.
Use scientific notation for very large/small magnitudes.
Remember rules: product/quotient/power of a power.

5) Common pitfalls

Misreading -2^2 (it’s -(2^2) = -4); use parentheses for (-2)^2 = 4.
Expecting real results for even roots of negatives.
Overflow/underflow when |x^y| is extreme.

6) Micro-examples

2^10 = 1024.
3^-2 = 1/9 ≈ 0.111111.
16^(1/2) = √16 = 4; 8^(1/3) = 2.
e^ln(2) = 2.

7) Mini-FAQ

Fractions as exponents? Yes, decimal or fraction works.
Very big results? We show scientific notation when helpful.
Complex values? This page focuses on real numbers.

8) Action tip

When results explode or vanish, switch to scientific notation or simplify with exponent rules first.