Index Laws

Index Laws

Definitions and Rules

  • Index laws or laws of exponents explain how to handle equations with variables raised to an exponent.
  • An exponent refers to the number of times a number or expression (the base) is multiplied by itself.
  • Base is the number or expression being multiplied.

Multiplication Law

  • When multiplying two numbers of the same base, add the exponents: a^n * a^m = a^(n + m).

Division Law

  • When dividing two numbers of the same base, subtract the exponents: a^n / a^m = a^(n - m).

Power of a Power Law

  • If an expression with an exponent is raised to another exponent, multiply the exponents: (a^n)^m = a^(n * m).

Zero Exponent

  • Any number (except 0) raised to the power of 0 equals 1: a^0 = 1.

Negative Exponents

  • Negative exponents result in the reciprocal of the base to the positive exponent: a^-n = 1/a^n.

Fractional Exponents

  • Fractional exponents signify roots. An exponent of a^(1/n) represents the nth root of a.

Remember to apply these rules carefully when simplifying and solving algebraic equations to avoid common mistakes and arrive at the correct solution.