Evaluate each exponential expression in Exercises 1–22. $2 squared times 2 cubed$

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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.

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.

Apply the property to the given expression: $2^2 \cdot 2^3 = 2^{2+3}$.

Simplify the exponent by adding: $2^{2+3} = 2^5$.

Express the final exponential form as \$2^5$, which is the simplified form of the original expression.

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주요 개념

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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.

Evaluate each exponential expression in Exercises 1–22. 22⋅232^2⋅2^3