Evaluate each exponential expression in Exercises 1–22. $2^2\cdot 2^3$

Verified step by step guidance

1. Identify the properties of exponents that apply to the expression \(2^2 \cdot 2^3\). Since the bases are the same (both are 2), you can use the product of powers property.
2. Recall the product of powers property: \(a^m \cdot a^n = a^{m+n}\). This means you add the exponents when multiplying with the same base.
3. Apply the property to the given expression: \(2^2 \cdot 2^3 = 2^{2+3}\).
4. Simplify the exponent by adding: \$2^{2+3} = 2^5$.
5. Express the final exponential form as \$2^5$, which is the simplified form of the original expression.

Key Concepts

Properties of Exponents

This concept involves the rules that govern how to manipulate expressions with exponents. For example, when multiplying powers with the same base, you add the exponents: a^m * a^n = a^(m+n). Understanding these properties is essential for simplifying exponential expressions.

Base and Exponent

An exponential expression consists of a base and an exponent, where the base is the number being multiplied, and the exponent indicates how many times the base is used as a factor. For example, in 2^3, 2 is the base and 3 is the exponent, meaning 2 multiplied by itself three times.

Evaluating Exponential Expressions

Evaluating an exponential expression means calculating its numerical value by performing the repeated multiplication indicated by the exponent. For instance, 2^3 equals 2 × 2 × 2 = 8. This step is necessary to find the final value of expressions like 2^2 * 2^3.