Chapter 1
Linear Equations and Graphing
Course: Gre
Subject: Gre Quantitative Reasoning
Chapter: Foundations Of Functions And Composition
Introduction: The Rules That Govern Powers
Exponents provide a shorthand for repeated multiplication. The properties of exponents (also called laws of exponents) establish consistent rules for simplifying expressions involving powers. Mastering these properties is essential for working with algebraic expressions, scientific notation, and exponential functions.
The Five Key Properties of Exponents
| Property | Formula | Description | | Product of Powers | x^m × x^n = x^(m + n) | Add exponents when multiplying same base | | Power to a Power | (x^m)^n = x^(m × n) | Multiply exponents when raising a power to a power | | Quotient of Powers | x^m / x^n = x^(m - n) | Subtract exponents when dividing same base | | Power of a Product | (xy)^m = x^m × y^m | Distribute exponent to each factor | | Power of a Quotient | (x/y)^m = x^m / y^m | Distribute exponent to numerator and denominator |