Evaluate each exponential expression in Exercises 1–22. 3^8/3^4

Verified step by step guidance

1. Identify the base and the exponents in the expression \( \frac{3^8}{3^4} \).
2. Recall the property of exponents: \( \frac{a^m}{a^n} = a^{m-n} \).
3. Apply this property to the expression: \( \frac{3^8}{3^4} = 3^{8-4} \).
4. Simplify the exponent: \( 8 - 4 \).
5. Rewrite the expression with the simplified exponent: \( 3^4 \).

Key Concepts

Exponential Expressions

Exponential expressions are mathematical expressions that involve a base raised to a power, indicating how many times the base is multiplied by itself. For example, in the expression 3^8, the base is 3, and the exponent is 8, meaning 3 is multiplied by itself 8 times. Understanding how to manipulate these expressions is crucial for evaluating them correctly.

Laws of Exponents

The laws of exponents are rules that govern the operations involving exponential expressions. One key law states that when dividing two exponential expressions with the same base, you subtract the exponents: a^m / a^n = a^(m-n). This principle is essential for simplifying expressions like 3^8/3^4, as it allows for straightforward calculations.

Simplification of Expressions

Simplification of expressions involves reducing complex expressions to their simplest form. In the context of exponential expressions, this often means applying the laws of exponents to combine or reduce terms. For instance, simplifying 3^8/3^4 results in 3^(8-4) = 3^4, which can then be further evaluated if needed.