Math Power Calculator
Calculate powers and exponents with step-by-step solutions
Calculate Mathematical Powers
The number being multiplied by itself
How many times to multiply the base
Power Formula
Calculation Result
Step-by-Step Solution:
Step 1: Identify the base and exponent
Base (b) = 2
Exponent (x) = 3
Step 2: Apply the power formula
Formula: b^x = 2^3
Step 3: Multiply base by itself 3 times
2^3 = 2 × 2 × 2 = 8
Example Calculations
Example 1: Basic Power
Problem: 2^3
Solution: 2^3 = 2 × 2 × 2 = 8
Explanation: Multiply the base (2) by itself 3 times
Example 2: Negative Exponent
Problem: 5^(-2)
Solution: 5^(-2) = 1/5^2 = 1/25 = 0.04
Explanation: Negative exponent means reciprocal with positive exponent
Example 3: Zero Exponent
Problem: 7^0
Solution: 7^0 = 1
Explanation: Any number (except 0) raised to power 0 equals 1
Example 4: Negative Base
Problem: (-3)^4
Solution: (-3)^4 = (-3) × (-3) × (-3) × (-3) = 81
Explanation: Even exponent with negative base gives positive result
Exponent Rules
Zero Exponent
a^0 = 1 (a ≠ 0)
Negative Exponent
a^(-n) = 1/a^n
Power of Power
(a^m)^n = a^(m×n)
Product Rule
a^m × a^n = a^(m+n)
Quotient Rule
a^m ÷ a^n = a^(m-n)
Quick Tips
Negative base with even exponent = positive result
Negative base with odd exponent = negative result
Any number to power 1 equals itself
Fractional exponents represent roots
Use parentheses for negative bases: (-2)^3 vs -2^3
Understanding Mathematical Powers
What are Powers?
Mathematical powers, also called exponents, represent repeated multiplication. In the expression a^n, 'a' is the base and 'n' is the exponent, meaning 'a' is multiplied by itself 'n' times.
Key Concepts
- •Base: The number being multiplied
- •Exponent: How many times to multiply
- •Power: The result of the calculation
- •Notation: a^n or an
Special Cases
Zero Exponent
Any non-zero number raised to power 0 equals 1
Negative Exponent
Represents the reciprocal of the positive exponent
Fractional Exponent
Represents roots: a^(1/n) = ⁿ√a
Real-World Applications
Science & Engineering
Powers are used in physics for area (length²), volume (length³), and in engineering for calculating compound growth, decay, and signal processing.
Finance & Economics
Compound interest calculations use powers to determine growth over time: A = P(1 + r)^t, where t is the time period exponent.
Computer Science
Powers of 2 are fundamental in computing for memory sizes, data structures, and algorithm complexity analysis.
Statistics
Powers appear in variance calculations, standard deviations, and probability distributions in statistical analysis.