Power & Exponent Calculator
Calculate powers and exponents instantly. Raise numbers to any power, including negative and fractional exponents. Perfect for algebra and scientific calculations.
Power & Exponent Calculator
How to Use This Calculator
Enter the base (the number being raised) and the exponent (the power). The calculator computes x^n using the formula: multiply the base by itself n times. Supports positive, negative, and fractional exponents.
Understanding Exponents
An exponent indicates how many times to multiply the base by itself. For example, 2ยณ = 2 ร 2 ร 2 = 8. The exponent is also called the power or index. The base can be any real number, and the exponent can be positive, negative, or fractional.
Special Exponent Rules
xโฐ = 1 (any number to power 0 is 1, except 0โฐ which is undefined). xยน = x (any number to power 1 is itself). xโปโฟ = 1/xโฟ (negative exponent means reciprocal). x^(1/n) = โฟโx (fractional exponent means root).
Common Applications
Used in compound interest calculations, exponential growth/decay, scientific notation, computer science (binary powers), physics equations, population growth models, and radioactive decay. Essential for understanding exponential relationships in nature and science.
Exponent Laws
Key laws: x^a ร x^b = x^(a+b) | x^a รท x^b = x^(a-b) | (x^a)^b = x^(aรb) | (xy)^a = x^a ร y^a | (x/y)^a = x^a / y^a. These laws simplify complex exponential expressions.
Frequently Asked Questions
Q: What’s 0โฐ? A: Undefined (mathematical debate). Q: Can base be negative? A: Yes, but odd/even exponents give different signs. Q: What’s e? A: Euler’s number โ 2.718, base of natural logarithm. Q: Largest power? A: Limited by computing precision, can overflow with large numbers.