Simplify each expression. See Example 1. 9³ • 9⁵

Verified step by step guidance

1. Recognize that the expression involves multiplication of powers with the same base: \(9^3 \cdot 9^5\).
2. Recall the exponent rule for multiplying powers with the same base: \(a^m \cdot a^n = a^{m+n}\).
3. Apply this rule by adding the exponents: \$9^{3+5}$.
4. Simplify the exponent sum: \$9^8$.
5. Express the simplified form as \$9^8$, which is the product of the original expression.

Key Concepts

Laws of Exponents

The laws of exponents govern how to simplify expressions involving powers. Specifically, when multiplying powers with the same base, you add their exponents. For example, a^m * a^n = a^(m+n). This rule is essential for simplifying expressions like 9³ • 9⁵.

Base and Exponent

In an expression like 9³, 9 is the base and 3 is the exponent, indicating how many times the base is multiplied by itself. Understanding the roles of base and exponent helps in applying exponent rules correctly during simplification.

Simplification of Exponential Expressions

Simplification involves rewriting expressions in a simpler or more compact form without changing their value. For exponential expressions, this often means combining like terms using exponent rules to reduce complexity and make calculations easier.