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

Verified step by step guidance

1. Recall the property of exponents that states when dividing powers with the same base, you subtract the exponents: \(a^{m} \div a^{n} = a^{m-n}\).
2. Identify the base and exponents in the expression \(3^{8} \div 3^{4}\). Here, the base is 3, the exponent in the numerator is 8, and the exponent in the denominator is 4.
3. Apply the exponent subtraction rule: \(3^{8} \div 3^{4} = 3^{8-4}\).
4. Simplify the exponent subtraction: \$3^{8-4} = 3^{4}$.
5. The expression simplifies to \$3^{4}$. To evaluate further, you would calculate \(3 \times 3 \times 3 \times 3\), but the problem only asks to simplify the expression.

Key Concepts

Properties of Exponents

This concept involves the rules that govern how to manipulate expressions with exponents. For example, when dividing powers with the same base, you subtract the exponents: a^m / a^n = a^(m-n). Understanding these properties allows simplification of exponential expressions efficiently.

Exponential Expressions

An exponential expression consists of a base raised to a power or exponent. Recognizing the base and exponent helps in applying the correct operations, such as multiplication or division of powers, and evaluating the expression accurately.

Simplification Techniques

Simplification involves reducing expressions to their simplest form by applying algebraic rules. In the context of exponents, this means using exponent properties to rewrite expressions in a more manageable form, making evaluation straightforward.