Starlight Tools

Exponent Calculator

Calculate xn with steps for positive, negative, decimal, and fractional exponents. You can also solve for a missing base or exponent; calculations run locally in your browser.

Enter fractions like 1/2, 3/4, or -2/3. Negative bases are interpreted as parenthesized: entering -4 means (-4).

Settings

Find exponent uses logarithms: \(n = \log(y) / \log(x)\). Find base uses roots: \(x = y^{1/n}\).

Result

Results will appear here.
Tool note: -4^2 normally means -(4^2), but an entered negative base here is treated as parenthesized, so base -4 and exponent 2 means (-4)^2.

What does xn mean?

Exponents are a compact way to describe repeated multiplication. The expression xn is read “x to the power of n.” For example, 34 means 3 × 3 × 3 × 3 = 81. This calculator can find the result of a power, the exponent that produces a result, or the base that produces a result.

Negative exponents flip a power into a reciprocal, so x-3 = 1 / x3. Fractional exponents connect to roots: x1/2 = sqrt(x) and x3/2 = sqrt(x3). The calculator accepts common fraction input such as 1/2, 3/4, and -2/3 so you do not need to convert them to decimals first.

Watch negative-base notation carefully. In standard order of operations, -42 means -(42) = -16, while (-4)2 = 16. When you type a negative base in this calculator, it is treated as parenthesized. A negative base with a fractional exponent may not have a real-number result, especially when the denominator is even.

How to use the exponent calculator

  1. Choose whether to find the result, exponent, or base.
  2. Enter the two known values. The missing field is disabled for the selected mode.
  3. Choose standard or scientific notation if you want a formatted output.
  4. Click calculate to see the answer, rule, steps, decimal value, and scientific notation.

Exponents show up everywhere: area and volume formulas (s2, s3), scientific notation (10n), compound growth in finance, and scale changes in science and engineering. Use the example chips to compare ordinary powers, reciprocals, roots, scientific notation, and repeated growth.

Maintained byStarlight Tools
Last reviewedJune 23, 2026
Numerical limitsUses browser JavaScript numbers, with decimal display capped at 12 places.
PrivacyInputs and results are calculated in your browser.

Exponent Laws

RuleFormulaExample
Product rulex^a * x^b = x^(a+b)2^3 * 2^4 = 2^7 = 128
Quotient rulex^a / x^b = x^(a-b)5^6 / 5^2 = 5^4 = 625
Power rule(x^a)^b = x^(a*b)(3^2)^4 = 3^8 = 6561
Power of a product(xy)^a = x^a y^a(2*5)^3 = 2^3 * 5^3 = 1000
Power of a quotient(x/y)^a = x^a / y^a(6/2)^3 = 6^3 / 2^3 = 27
Negative exponentx^-a = 1 / x^a2^-4 = 1 / 16 = 0.0625
Zero exponentx^0 = 1, x != 08^0 = 1
Exponent of 1x^1 = x12^1 = 12
Fractional exponentx^(a/b) = b-root(x^a)27^(2/3) = cuberoot(27^2) = 9

Exponent FAQ

What is an exponent?

An exponent tells how many times to use the base as a factor. \(4^3\) means \(4 * 4 * 4\).

How do negative exponents work?

They make a reciprocal: \(x^{-n} = 1/x^n\), as long as \(x\) is not zero.

What is x0?

For any nonzero \(x\), \(x^0 = 1\). This follows from the quotient rule \(x^a / x^a = x^0 = 1\).

What is 00?

It depends on context, but this calculator marks \(0^0\) as undefined to avoid mixing conventions.

How do fractional exponents work?

\(x^{1/2}\) is \(\sqrt{x}\), and \(x^{3/2}\) is \(\sqrt{x^3}\). In general, \(x^{a/b}\) is the b-th root of \(x^a\).

How do you multiply or divide exponents?

With the same base, add exponents when multiplying and subtract exponents when dividing: \(x^a x^b = x^{a+b}\), \(x^a/x^b = x^{a-b}\).

Why does -42 differ from (-4)2?

Without parentheses, the exponent applies before the negative sign: \(-4^2 = -16\). With parentheses, the negative base is squared: \((-4)^2 = 16\).

How do you find an unknown exponent?

For a positive base \(b\) not equal to 1 and positive result \(y\), solve \(b^n = y\) with \(n = \log(y) / \log(b)\).

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