Exponent Calculator
Calculate xy (x to the power of y)
Exponent Rules
x a × x b = x a+b
Example: 2³ × 2² = 2⁵ = 32
x a ÷ x b = x a-b
Example: 2⁵ ÷ 2² = 2³ = 8
(x a)b = x ab
Example: (2³)² = 2⁶ = 64
x 0 = 1
Any number to the power 0 equals 1
x -a = 1/x a
Example: 2⁻³ = 1/2³ = 1/8 = 0.125
x 1/2 = √x
Example: 161/2 = √16 = 4
Examples
Example 1: 2³
2³ = 2 × 2 × 2
= 8
Example 2: 5⁴
5⁴ = 5 × 5 × 5 × 5
= 625
Example 3: 10⁻²
10⁻² = 1/10² = 1/100
= 0.01
Example 4: 41/2
41/2 = √4
= 2
About Exponents
An exponent (or power) indicates how many times a number (the base) is multiplied by itself. For example, 2³ means 2 × 2 × 2 = 8.
Special Exponents
- x¹ = x (any number to power 1 is itself)
- x⁰ = 1 (any non-zero number to power 0 is 1)
- 1ˣ = 1 (1 to any power is 1)
- 0ˣ = 0 (for positive x)
Applications
- Compound Interest: A = P(1 + r)t
- Population Growth: Exponential models
- Physics: Radioactive decay, wave functions
- Computer Science: Algorithm complexity (O(2ⁿ))
- Engineering: Signal processing, electronics
How to Use This Calculator
Enter Base
Input the base number (x) that will be raised to a power. This can be any real number.
Enter Exponent
Input the exponent (y) - the power to which the base is raised. This can be any real number: positive, negative, or zero.
Calculate
Click "Calculate x^y" to compute the result. The answer will be displayed in both standard form and scientific notation.
Formula
xy = x × x × ... × x (y times)
Where:
- x = base number
- y = exponent (power)
- xy = x raised to the power of y
Example 1: 2³
2³ = 2 × 2 × 2 = 8
Example 2: 5⁴
5⁴ = 5 × 5 × 5 × 5 = 625
Example 3: 10⁻²
10⁻² = 1/10² = 1/100 = 0.01
About Exponent Calculator
The Exponent Calculator helps you calculate x raised to the power of y (xy). An exponent indicates how many times a number (the base) is multiplied by itself. This calculator supports any base and exponent, including negative exponents and fractional exponents, making it useful for a wide range of mathematical, scientific, and engineering calculations.
When to Use This Calculator
- Mathematics: Calculate powers for algebra, calculus, and number theory problems
- Science: Compute scientific notation, exponential growth, and decay
- Engineering: Solve problems involving exponential functions and power calculations
- Finance: Calculate compound interest and investment returns
- Computer Science: Work with exponential complexity and algorithm analysis
Why Use Our Calculator?
- ✅ Instant Results: Get accurate calculations immediately
- ✅ All Exponent Types: Supports positive, negative, fractional, and zero exponents
- ✅ Scientific Notation: Automatically displays very large or small results in scientific notation
- ✅ Easy to Use: Simple interface for all skill levels
- ✅ 100% Free: No registration or payment required
- ✅ Educational: Learn exponent rules through examples and calculations
Common Applications
Compound Interest: If you invest $1,000 at 5% annual interest for 10 years: A = 1000 × (1.05)10 ≈ $1,628.89.
Population Growth: If a population doubles every year, after 5 years: P = P₀ × 25 = P₀ × 32 (32 times the initial population).
Scientific Notation: Express very large numbers like 6,000,000 as 6 × 10⁶.
Tips for Best Results
- Remember: x⁰ = 1 for any x (except 0⁰ which is undefined)
- Remember: x⁻ⁿ = 1/xⁿ (negative exponents represent reciprocals)
- Remember: x1/n = ⁿ√x (fractional exponents represent roots)
- Very large positive exponents give very large results
- Very large negative exponents give values very close to zero
Frequently Asked Questions
What is 0⁰?
This is mathematically undefined or conventionally defined as 1 in some contexts. It is a subject of mathematical debate.
Can exponents be negative?
Yes! A negative exponent means reciprocal: x⁻ⁿ = 1/xⁿ. For example, 2⁻³ = 1/8.
Can exponents be fractions?
Yes! Fractional exponents represent roots: x 1/n = ⁿ√x. For example, 81/3 = ³√8 = 2.
What is the difference between 2³ and 3²?
2³ = 8 (multiply 2 three times), while 3² = 9 (multiply 3 two times). The order matters!
How do I calculate large exponents?
Use this calculator! For very large results, scientific notation is displayed automatically.