Rules of Exponents Study Guide

Exponents are a shorthand way of expressing repeated multiplication. The rules of exponents help us simplify and manipulate expressions involving exponents. Here are the key rules to remember:

Rule 1: Product of Powers

When multiplying two powers with the same base, you add the exponents:

a^m * aⁿ = a^m+n

Rule 2: Quotient of Powers

When dividing two powers with the same base, you subtract the exponents:

a^m / aⁿ = a^m-n

Rule 3: Power of a Power

When raising a power to another power, you multiply the exponents:

(a^m)ⁿ = a^m*n

Rule 4: Power of a Product

When raising a product to a power, you distribute the power to each factor:

(ab)ⁿ = aⁿ * bⁿ

Rule 5: Power of a Quotient

When raising a quotient to a power, you distribute the power to the numerator and denominator:

(a/b)ⁿ = aⁿ / bⁿ

Rule 6: Zero Exponent

Any non-zero number raised to the power of 0 is equal to 1:

a⁰ = 1

Rule 7: Negative Exponent

A negative exponent indicates the reciprocal of the base raised to the positive exponent:

a^-n = 1 / aⁿ

These rules are fundamental for simplifying and solving problems involving exponents. Practice applying these rules to various exponent expressions to solidify your understanding.