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HomeCalculatorsConvertersFormula Library
Home/Formula Library/Exponentiation

Exponentiation

Relate a base, an exponent, and a power — fill any two to solve for the third.

General

  • Percentage proportion
  • Percent error
  • Ratio and proportion
  • Rounding
  • Exponentiation
  • Nth root
  • Fraction arithmetic
  • Long division
  • Order of operations (PEMDAS)

Formula

base^exponent = result

Explanation

Exponentiation multiplies the base by itself exponent times (for positive integers). Logarithms invert the relation when solving for the exponent. Negative bases with fractional exponents may be undefined in reals.

Variables

  • basethe number being raised
  • exponentthe power
  • resultbase raised to the exponent

When to use

Growth/decay, scientific notation, compound interest models, and algebra homework.

Use this formula

Calculators

  • Exponent Calculator→

Related formulas

  • Nth rootⁿ√a = b ⇔ bⁿ = a
  • Scientific notationRewrite as significand × 10^exponent (normalized scientific form)

Other categories

  • Statistics
  • Cooking & apparel
  • Data & digital
  • Electricity & magnetism
  • Encodings & numbers
  • Date & time
Formula Library→

Popular

  • Percentage proportion
  • Arithmetic and weighted mean
  • Fraction arithmetic
  • Number base conversion
Formula Library→