Exponent Calculator
Calculate exponents and powers with optional logarithmic results.
What are the rules of exponents?
Key rules: x^a x x^b = x^(a+b); x^a / x^b = x^(a-b); (x^a)^b = x^(ab); x^0 = 1; x^(-a) = 1/x^a; x^(1/2) = sqrtx. Examples: 2^3 x 2^2 = 2⁵ = 32; 2^3 / 2^2 = 2^1 = 2; (2^3)^2 = 2⁶ = 64; 2^(-2) = 1/4. These rules simplify complex calculations and are fundamental in algebra.
What is a negative exponent?
Negative exponent means "reciprocal". x^(-n) = 1/x^n. Examples: 2^(-3) = 1/2^3 = 1/8 = 0.125; 10^(-2) = 1/100 = 0.01. Used in scientific notation: 0.001 = 10^(-3). In chemistry: pH scale uses negative logs. In finance: Discount factors use negative exponents. Not negative number - it's position (denominator vs numerator).
What is a fractional exponent?
Fractional exponent = root. x^(1/n) = ⁿsqrtx. Examples: 16^(1/2) = sqrt16 = 4; 8^(1/3) = cbrt8 = 2; 16^(3/4) = (⁴sqrt16)^3 = 2^3 = 8. Generally: x^(m/n) = (ⁿsqrtx)^m or ⁿsqrt(x^m). Useful in growth calculations, physics formulas, and compound interest. Calculator handles decimals for fractional powers.
What is exponential growth vs linear growth?
Linear: Add same amount each period (1, 2, 3, 4, 5...). Exponential: Multiply by same factor (1, 2, 4, 8, 16...). Example: $100 at 10% - Linear: $110, $120, $130 (add $10). Exponential: $110, $121, $133 (multiply by 1.1). Exponential accelerates dramatically. Seen in: compound interest, population growth, viral spread, Moore's Law (computing power doubles).