Simplify each expression. See Example 1. 9³ • 9⁵

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Recognize that the expression involves multiplication of powers with the same base: $9^3 \cdot 9^5$.

Recall the exponent rule for multiplying powers with the same base: $a^m \cdot a^n = a^{m+n}$.

Apply this rule by adding the exponents: $9^{3+5}$.

Simplify the exponent sum: \$9^8$.

Express the simplified form as \$9^8$, which is the product of the original expression.

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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.

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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.

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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.

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