Power Function Calculator
Calculate any number raised to any power with step-by-step solutions and detailed explanations
Calculate Power Function: f(x) = b^x
The number to be raised to a power
The power to which the base is raised
Power Function Results
Example Calculations
Positive Integer Exponent
Example: 2³
Calculation: 2 × 2 × 2 = 8
Result: 8
Negative Exponent
Example: 3⁻²
Calculation: 1/(3²) = 1/9
Result: 0.111111...
Zero Exponent
Example: 5⁰
Rule: Any number⁰ = 1
Result: 1
Decimal Exponent
Example: 4⁰·⁵
Calculation: √4
Result: 2
Power Function Rules
Zero Exponent
a⁰ = 1 (for a ≠ 0)
First Power
a¹ = a
Negative Exponent
a⁻ⁿ = 1/aⁿ
Fractional Exponent
a^(m/n) = ⁿ√(aᵐ)
Product Rule
aᵐ × aⁿ = a^(m+n)
Quotient Rule
aᵐ ÷ aⁿ = a^(m-n)
Quick Presets
Understanding Power Functions
What is a Power Function?
A power function is a mathematical function of the form f(x) = b^x, where b is the base and x is the exponent. The exponent determines how many times the base is multiplied by itself.
Types of Exponents
- •Positive integers: Repeated multiplication (e.g., 2³ = 2×2×2)
- •Zero: Always equals 1 (except 0⁰)
- •Negative: Reciprocal of positive power
- •Fractions: Roots and powers combined
Important Rules
Zero Exponent Rule
Any non-zero number raised to the power of 0 equals 1
a⁰ = 1 (where a ≠ 0)
Negative Exponent Rule
A negative exponent means taking the reciprocal
a⁻ⁿ = 1/aⁿ
Fractional Exponent Rule
A fractional exponent represents roots
a^(1/n) = ⁿ√a
Applications
- •Scientific calculations and measurements
- •Exponential growth and decay models
- •Computer science and algorithms
- •Financial calculations (compound interest)
Special Cases and Notes
Undefined Cases
- • 0⁰ is mathematically undefined
- • 0 raised to any negative power is undefined
- • Division by zero in negative exponents
Large Numbers
- • Results may be displayed in scientific notation
- • Very large numbers may exceed calculation limits
- • Decimal precision may be limited for very small results