Simplify each expression. See Example 1. (9^3)(9^5)

Key Concepts

Properties of Exponents

The properties of exponents are rules that govern how to manipulate expressions involving powers. One key property is that when multiplying two expressions with the same base, you add their exponents. For example, a^m * a^n = a^(m+n). This property is essential for simplifying expressions like (9^3)(9^5).

Base and Exponent

In an expression of the form a^n, 'a' is called the base and 'n' is the exponent. The base indicates the number being multiplied, while the exponent shows how many times the base is used as a factor. Understanding the roles of base and exponent is crucial for simplifying expressions and performing calculations correctly.

Simplification of Expressions

Simplification involves rewriting an expression in a more concise or manageable form without changing its value. In the context of exponents, this often means applying exponent rules to combine terms. For instance, simplifying (9^3)(9^5) results in 9^(3+5) = 9^8, demonstrating how simplification can lead to clearer results.