Exponent Calculator
Calculate powers and exponents with step-by-step solutions
Expression:
=
Result
As Fraction:
/
Step-by-Step Solution
Squared Result
result²
Square Root of Result
√result
Reciprocal
1/result
Exponent Rules Reference
| Rule Name | Formula | Example |
|---|---|---|
Powers of 2 Reference
Powers of 10 Reference
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About Exponent Calculator
What is an Exponent Calculator?
An exponent calculator is a mathematical tool that computes the result of raising a base number to a specific power (exponent). Exponentiation is one of the fundamental operations in mathematics, representing repeated multiplication of a number by itself.
How to Use This Calculator
- Enter the base number: This is the number that will be multiplied
- Enter the exponent: This determines how many times the base is multiplied
- View instant results: Get the calculated power with step-by-step explanation
- Explore exponent rules: Learn the mathematical properties of exponents
Understanding Exponents
Basic Concept
In the expression b^n (b to the power of n):
- Base (b): The number being multiplied
- Exponent (n): The number of times the base is used as a factor
Example: 3^4 = 3 × 3 × 3 × 3 = 81
Key Exponent Rules
1. Product Rule
When multiplying with the same base, add exponents:
- a^m × a^n = a^(m+n)
- Example: 2³ × 2² = 2⁵ = 32
2. Quotient Rule
When dividing with the same base, subtract exponents:
- a^m ÷ a^n = a^(m-n)
- Example: 5⁴ ÷ 5² = 5² = 25
3. Power of a Power
When raising a power to another power, multiply exponents:
- (a^m)^n = a^(m×n)
- Example: (3²)³ = 3⁶ = 729
4. Zero Exponent Rule
Any non-zero number raised to zero equals 1:
- a⁰ = 1 (where a ≠ 0)
- Example: 25⁰ = 1
5. Negative Exponent Rule
A negative exponent means take the reciprocal:
- a^(-n) = 1/a^n
- Example: 10⁻³ = 1/1000 = 0.001
6. Fractional Exponents
Fractional exponents represent roots:
- a^(1/n) = ⁿ√a (nth root of a)
- a^(m/n) = ⁿ√(a^m)
- Example: 64^(1/3) = ³√64 = 4
Common Applications
- Scientific notation: Representing very large or small numbers
- Compound interest: Financial calculations
- Population growth: Exponential growth models
- Computer science: Binary calculations and algorithms
- Physics: Decay rates and energy calculations
Frequently Asked Questions
What is 0 raised to any power?
0 raised to any positive power equals 0. However, 0⁰ is undefined or sometimes defined as 1 depending on the context.
Can you have a negative base with a fractional exponent?
Negative bases with fractional exponents can result in complex numbers. This calculator handles real number results.
What happens with very large exponents?
With very large exponents, results can exceed the maximum number that can be represented, resulting in infinity.
Tip: Use this calculator to verify your manual calculations and understand the step-by-step process of exponentiation.