An exponent indicates how many times a number (the base) is multiplied by itself. For example, 2³ = 2 × 2 × 2 = 8. The exponent (3) tells us to multiply the base (2) by itself 3 times.

How do negative exponents work?

A negative exponent means you take the reciprocal of the base raised to the positive exponent. For example, 2⁻³ = 1/2³ = 1/8 = 0.125. The rule is: x⁻ⁿ = 1/xⁿ.

What are fractional exponents?

Fractional exponents represent roots. x^(1/n) is the nth root of x. For example, 8^(1/3) = ³√8 = 2 (cube root of 8). More generally, x^(m/n) = (ⁿ√x)^m.

What is the difference between exponential growth and decay?

Exponential growth occurs when a quantity increases by a fixed percentage over time (rate > 0), like compound interest. Exponential decay occurs when a quantity decreases by a fixed percentage (rate < 0), like radioactive decay. Both use the formula: P(t) = P₀ × (1 + r)^t.

What are the basic exponent rules?

Key exponent rules: 1) x^m × x^n = x^(m+n), 2) x^m ÷ x^n = x^(m-n), 3) (x^m)^n = x^(m×n), 4) x^0 = 1, 5) x^(-n) = 1/x^n, 6) x^(1/n) = ⁿ√x.

Why is any number raised to the power of 0 equal to 1?

By the division rule of exponents: x^n ÷ x^n = x^(n-n) = x^0. Since any non-zero number divided by itself equals 1, x^0 = 1. This is true for all x ≠ 0.

Exponent Calculator

Calculate powers and exponents including squares, cubes, negative exponents, and fractional powers. Get step-by-step solutions with exponent rules explained.

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superscript Exponent Calculator

Calculation Type

Base (x)

Exponent (n)

Can be negative or fractional

Decimal Places

calculate 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

Input Values

Calculation Type

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Base (x)

Exponent (n)

Decimal Places

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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 This 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.

superscript

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

Any number raised to the power of 0 equals 1 (except 0⁰ which is undefined)

Negative exponents create fractions: x⁻ⁿ = 1/xⁿ

Fractional exponents are roots: x^(1/2) = √x, x^(1/3) = ∛x

When multiplying same bases, add exponents: xᵃ × xᵇ = x^(a+b)

When dividing same bases, subtract exponents: xᵃ ÷ xᵇ = x^(a-b)

For exponential growth, use the formula: Final = Initial × (1 + rate)^time

Exponent & Power Calculator

Calculate powers, roots, squares, cubes, and exponential functions with ease. Supports negative exponents, fractional powers, and exponential growth/decay calculations with detailed steps.

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.

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.