Exponent Calculator
Calculate any base raised to any exponent. See results in standard and scientific notation, plus the inverse (negative exponent).
Result
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Scientific Notation —
Inverse (Base^−Exp) —
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Result
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Scientific Notation —
Inverse (base^−n) —
log₁₀ of Result —
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Multi-Base Results
Results for Each Base —
Largest Result —
Smallest Result —
Combined Operations
Product of All Results —
Ratio: B1^E1 / B2^E2 —
log₁₀ Sum —
How to Use This Calculator
Enter a Base number and an Exponent. The calculator returns the result in standard form, scientific notation, and the inverse (base raised to the negative exponent).
Formula
bⁿ = b × b × … (n times) • b⁻ⁿ = 1 / bⁿ
Example
2¹⁰ = 1024 = 1.0240×10³, 2⁻¹⁰ ≈ 0.0009766
Frequently Asked Questions
- An exponent (also called a power) tells you how many times to multiply the base by itself. In the expression b^n, b is the base and n is the exponent. For example, 2³ = 2 × 2 × 2 = 8, and 5⁴ = 5 × 5 × 5 × 5 = 625. Exponents are a shorthand for repeated multiplication. They obey key rules: b^m × b^n = b^(m+n), (b^m)^n = b^(mn), and b^m / b^n = b^(m−n). Understanding these rules lets you simplify complex expressions without a calculator.
- A negative exponent means the reciprocal of the base raised to the positive exponent: b⁻ⁿ = 1 / bⁿ. For example, 2⁻³ = 1/2³ = 1/8 = 0.125, and 10⁻⁴ = 1/10,000 = 0.0001. Negative exponents are commonly seen in scientific notation for very small numbers, unit conversions (e.g., cm⁻¹ in spectroscopy), and decay formulas. A common mistake is thinking b⁻ⁿ is negative — it is always positive when b > 0, just a small fraction.
- Any non-zero number raised to the power of 0 equals 1. For example, 7⁰ = 1, (−4)⁰ = 1, and (0.5)⁰ = 1. This rule follows from the quotient rule: b^n / b^n = b^(n−n) = b⁰, and any number divided by itself equals 1. The expression 0⁰ is mathematically indeterminate — it equals 1 in combinatorics and limits but is undefined in analysis. The calculator returns 1 for 0⁰ following the convention used in combinatorics.
- A fractional exponent represents a root: b^(1/n) = ⁿ√b (the nth root of b). For example, 8^(1/3) = ∛8 = 2, and 16^(1/4) = ∜16 = 2. In general, b^(m/n) = (ⁿ√b)^m. For instance, 27^(2/3) = (∛27)² = 3² = 9. Fractional exponents unify the notation for powers and roots, making algebraic manipulation easier. Always evaluate the root first, then the power, to keep numbers manageable.
- Scientific notation expresses numbers as a × 10ⁿ, where 1 ≤ |a| < 10 and n is an integer. This is useful for very large or very small numbers. For example, 1,024 = 1.024 × 10³ and 0.000042 = 4.2 × 10⁻⁵. To convert to scientific notation, move the decimal point until only one non-zero digit is to the left of it — the number of places moved becomes the exponent (positive if you moved left, negative if right). This calculator shows results in both standard form and scientific notation automatically.