Exponent Calculator

Exponentiation is a mathematical operation that involves raising a base number to a certain power (exponent). It's written as b^n, where b is the base and n is the exponent. The result is b multiplied by itself n times.

Exponent Rules:

• Product Rule: a^m × a^n = a^(m+n)
• Quotient Rule: a^m ÷ a^n = a^(m-n)
• Power Rule: (a^m)^n = a^(m×n)
• Zero Exponent: a^0 = 1 (where a ≠ 0)
• Negative Exponent: a^(-n) = 1/a^n
• Fractional Exponent: a^(m/n) = n√(a^m)

Common Examples:

• 2^3 = 2 × 2 × 2 = 8
• 5^2 = 5 × 5 = 25
• 10^4 = 10,000
• 3^(-2) = 1/3^2 = 1/9
• 16^(1/2) = √16 = 4

Applications:

• Compound interest calculations
• Population growth modeling
• Scientific notation
• Computer science and algorithms
• Physics and engineering calculations
• Cryptography and security