Understanding Exponents
An exponent indicates how many times a number (the base) is multiplied by itself. For example, 2³ = 2 × 2 × 2 = 8. Exponents are fundamental in mathematics, science, and computing.
Exponent Calculator
Exponents appear everywhere in science, engineering, and finance. Use this calculator to compute any power — positive, negative, fractional, or zero — instantly. Whether you are calculating compound interest (A = P(1+r)^n), converting scientific notation, solving physics equations, or working with decibels and logarithmic scales, understanding powers is fundamental. The calculator handles edge cases like zero exponents (n⁰ = 1), negative bases, and fractional exponents (square roots, cube roots) without needing manual formula lookup.
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Exponent Calculator calculator
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Exponent Calculator
Can be negative or fractional
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Result
Expression
210
Result
1024
Scientific Notation
1.024 × 10³
Formula Used
xⁿ
Step-by-Step
2¹⁰ = 2×2×2×2×2×2×2×2×2×2
= 1024
Exponent Rules
x⁰ = 1
x⁻ⁿ = 1/xⁿ
xᵃ·xᵇ = xᵃ⁺ᵇ
x^(1/n) = ⁿ√x
lightbulb Tips
- •x⁰ = 1 (any x ≠ 0)
- •x⁻ⁿ = 1/xⁿ
- •x^(1/n) = ⁿ√x
- •xᵃ × xᵇ = xᵃ⁺ᵇ
superscript Reference
Powers of 2
2¹ = 22⁶ = 64
2² = 42⁷ = 128
2³ = 82⁸ = 256
2⁴ = 162⁹ = 512
2⁵ = 322¹⁰ = 1024
Growth Formula
P(t) = P₀ × (1 + r)^t
How to Use the Exponent Calculator
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Choose Calculation Type
Select power, square, cube, root, or exponential growth/decay.
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Enter Base Number
Input the base number you want to raise to a power.
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Enter Exponent
Input the exponent (can be negative or fractional).
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View Results
See the result with step-by-step explanation and scientific notation.
The Formula
An exponent tells you how many times to multiply the base by itself. For negative exponents, take the reciprocal. For fractional exponents, calculate roots.
xⁿ = x × x × x × ... (n times)
lightbulb Variables Explained
- x Base number
- n Exponent (power)
- xⁿ x raised to the power n
tips_and_updates Pro Tips
1
Any number raised to the power of 0 equals 1 (except 0⁰ which is undefined)
2
Negative exponents create fractions: x⁻ⁿ = 1/xⁿ
3
Fractional exponents are roots: x^(1/2) = √x, x^(1/3) = ∛x
4
When multiplying same bases, add exponents: xᵃ × xᵇ = x^(a+b)
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When dividing same bases, subtract exponents: xᵃ ÷ xᵇ = x^(a-b)
6
For exponential growth, use the formula: Final = Initial × (1 + rate)^time
Calculate powers, roots, squares, cubes, and exponential functions with ease. Supports negative exponents, fractional powers, and exponential growth/decay calculations with detailed steps.
Negative and Fractional Exponents
Negative exponents create reciprocals: 2⁻³ = 1/8. Fractional exponents represent roots: 8^(1/3) = 2 (cube root of 8). These extend the power of exponents beyond simple repeated multiplication.
Exponential Growth and Decay
Exponential functions model real-world phenomena like population growth, compound interest, and radioactive decay. The formula P(t) = P₀ × (1 + r)^t describes how quantities change over time.