Simplify each expression. (9³)(9⁵)

Verified step by step guidance

1. Identify the base and the exponents in the expression \((9^{3})(9^{5})\). Here, the base is 9 for both terms.
2. Recall the exponent rule for multiplication with the same base: \(a^{m} \times a^{n} = a^{m+n}\).
3. Apply the rule by adding the exponents: \(9^{3} \times 9^{5} = 9^{3+5}\).
4. Simplify the exponent sum: \$9^{3+5} = 9^{8}$.
5. Write the simplified expression as \$9^{8}$, which is the product of the original terms expressed with a single exponent.

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 (9^3)(9^5).

Base and Exponent

In an expression like 9^3, 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 bases using exponent rules to reduce the expression to a single power.