This tool computes the value of any number raised to a given power. Simply enter a base and an exponent, and the calculator will display the result along with the calculation steps. Ideal for students, engineers, and anyone working with powers, this tool supports both integers and decimals.
Exponentiation Calculator
xn = a
Base Number (x)
Exponent (n)
Result (a)
How to Use This Calculator
- Enter Base (x): Type the number you want to raise to a power.
- Enter Exponent (n): Type the power to which the base should be raised.
- View Result (a): The result is automatically calculated and displayed.
- Check Steps: A breakdown of the calculation appears below the result.
- Copy Result: Click “Copy Result” to save the output to your clipboard.
- Clear: Click “Clear All” to reset all fields and start a new calculation.
Table of Values
| x | x² | x³ | x⁴ | x⁵ |
| 1 | 1 | 1 | 1 | 1 |
| 2 | 4 | 8 | 16 | 32 |
| 3 | 9 | 27 | 81 | 243 |
| 4 | 16 | 64 | 256 | 1024 |
| 5 | 25 | 125 | 625 | 3125 |
| 6 | 36 | 216 | 1296 | 7776 |
| 7 | 49 | 343 | 2401 | 16807 |
| 8 | 64 | 512 | 4096 | 32768 |
| 9 | 81 | 729 | 6561 | 59049 |
| 10 | 100 | 1000 | 10000 | 100000 |
Understanding Exponentiation
Exponentiation is a mathematical operation that involves raising a base number (x) to the power of an exponent (n). It is written as xⁿ and means multiplying the base by itself n times. For example, 3² = 3 × 3 = 9.
Basic Concept
In the expression xⁿ:
- x is the base — the number being multiplied.
- n is the exponent — it tells how many times the base is multiplied by itself.
- a is the result — the final value of the operation.
What is a Negative Exponent?
A negative exponent means the reciprocal of the base raised to the opposite positive power. For example:
- 2⁻¹ = 1 / 2¹ = 1/2
- 3⁻² = 1 / (3²) = 1/9
In general, x⁻ⁿ = 1 / xⁿ for any non-zero base x.
What is a Decimal or Fractional Exponent?
Decimal or fractional exponents represent roots. For example:
- x0.5 = √x (square root of x)
- x0.25 = ⁴√x (fourth root of x)
- x1.5 = x × √x
In general, xm/n means the n-th root of x raised to the m-th power: xm/n = (ⁿ√x)m.
Special Exponents
- x⁰ = 1 for any non-zero x (by definition).
- 1ⁿ = 1 for any exponent n.
- 0ⁿ = 0 for any positive exponent n.
Applications of Exponentiation
Exponentiation is used in many fields such as:
- Compound interest calculations in finance
- Scientific notation for very large or small numbers
- Physics and engineering formulas
- Computer science for algorithm complexity
Important Notes
- Negative bases with fractional exponents may result in complex numbers.
- Zero raised to a negative or zero exponent is undefined.
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