Calculate powers and exponents instantly with our free online calculator
An exponent represents repeated multiplication. The formula is: base^exponent, which means multiplying the base by itself the number of times indicated by the exponent. For example, 2^4 = 2 × 2 × 2 × 2 = 16. The calculator uses JavaScript's Math.pow() function for precise computation of both positive and negative exponents.
Exponents are fundamental in mathematics, science, engineering, and finance. They represent exponential growth (population, investments), decay (radioactive half-life), area and volume calculations, compound interest, scientific notation, and many natural phenomena. Understanding exponents is essential for higher mathematics and real-world problem solving.
Positive exponents: Multiply the base by itself (2³ = 8). Negative exponents: Take the reciprocal (2⁻³ = 1/8). Zero exponent: Any non-zero number to the power of 0 equals 1 (2⁰ = 1). Fractional exponents: Represent roots (4^(1/2) = √4 = 2). These rules form the foundation of algebraic manipulation.
Memorize common powers (2^10 = 1024, 3^4 = 81) for quick mental math. When multiplying same bases, add exponents (2³ × 2² = 2⁵). When dividing, subtract exponents. Use scientific notation for very large or small numbers. Remember that exponential growth becomes extremely rapid - doubling 10 times increases a value by over 1000x.
Exponents represent repeated multiplication of a base number by itself. The expression b^n means multiplying b by itself n times. For example, 2^4 = 2 x 2 x 2 x 2 = 16. The base is the number being multiplied, and the exponent (or power) tells you how many times to multiply it.
A negative exponent means you take the reciprocal of the base raised to the positive version of that exponent. For example, 2^(-3) = 1/(2^3) = 1/8 = 0.125. In general, b^(-n) = 1/(b^n). Negative exponents do not make the result negative; they create a fraction.
Any non-zero number raised to the power of 0 equals 1. For example, 5^0 = 1, 100^0 = 1, and (-3)^0 = 1. This rule follows from the pattern of dividing by the base: since 2^3 = 8, 2^2 = 4, 2^1 = 2, each step divides by 2, so 2^0 = 1. The expression 0^0 is generally considered indeterminate in mathematics.