Evaluate each exponential expression in Exercises 1–22. 2^2⋅2^3

Verified step by step guidance

1. Identify the base and the exponents in the expression: The base is 2, and the exponents are 2 and 3.
2. Use the property of exponents that states \(a^m \cdot a^n = a^{m+n}\).
3. Apply this property to the expression \(2^2 \cdot 2^3\) to combine the exponents.
4. Add the exponents: \(2 + 3\).
5. Rewrite the expression as a single power of 2 using the sum of the exponents.

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 2^3, the base is 2 and the exponent is 3, meaning 2 is multiplied by itself three times (2 × 2 × 2). Understanding how to manipulate these expressions is crucial for evaluating them correctly.

Properties of Exponents

The properties of exponents are rules that simplify the operations involving exponential expressions. One key property is that when multiplying two expressions with the same base, you add the exponents: a^m × a^n = a^(m+n). This property allows for easier calculations and is essential for evaluating expressions like 2^2 ⋅ 2^3.

Simplification of Expressions

Simplification of expressions involves reducing complex expressions to their simplest form. In the context of exponential expressions, this means applying the properties of exponents to combine terms efficiently. For instance, using the property of exponents, 2^2 ⋅ 2^3 simplifies to 2^(2+3) = 2^5, which can then be evaluated to find the final numerical result.