Exponent Calculator
Calculate powers and exponents with our free online calculator. Enter any base number and exponent to get instant results with step-by-step explanations.
Exponent Calculator
Exponent Calculator
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What is Exponentiation?
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
Frequently Asked Questions
What is an exponent?
An exponent tells you how many times to multiply a base by itself. In 2^5, the base 2 is multiplied five times: 2 × 2 × 2 × 2 × 2 = 32.
What does a negative exponent mean?
A negative exponent is the reciprocal of the positive power: 2^-3 = 1 / 2^3 = 1/8 = 0.125.
What does an exponent of 0 equal?
Any non-zero number raised to the power of 0 equals 1. For example, 7^0 = 1 and 100^0 = 1.
What is a fractional exponent?
A fractional exponent is a root: x^(1/2) is the square root of x, and x^(1/3) is the cube root. So 27^(1/3) = 3.