Simplify each expression. See Example 1. (9³)(9⁵)

Verified step by step guidance

1. Recall the property of exponents that states when multiplying powers with the same base, you add the exponents: \(a^m \times a^n = a^{m+n}\).
2. Identify the base and exponents in the expression \((9^3)(9^5)\). Here, the base is 9, and the exponents are 3 and 5.
3. Apply the exponent rule by adding the exponents: \$9^{3+5}$.
4. Simplify the exponent sum: \$9^8$.
5. The expression is now simplified to \$9^8$, which is the product of the original expression.

Key Concepts

Laws of Exponents

The laws of exponents provide rules for simplifying expressions involving powers. One key rule states that when multiplying two expressions 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 (9^3)(9^5).

Base and Exponent

In an expression like 9^3, 9 is the base and 3 is the exponent. The exponent indicates 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 Expressions

Simplification involves rewriting an expression in a simpler or more compact form without changing its value. For exponential expressions, this often means applying exponent rules to combine terms, making the expression easier to understand or use in further calculations.