# 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.