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Chapter 0: Problem 13

Evaluate each exponential expression. $$2^{2} \cdot 2^{3}$$

Short Answer

Expert verified
The result of the evaluation of the exponential expression \(2^{2} \cdot 2^{3}\) is 32.

Step by step solution

01

Identify the base and apply the law of exponent

In the given expression \(2^{2} \cdot 2^{3}\), the base is 2 and we're multiplying two expressions with the same base. Hence, apply the product of powers law or multiplicative law of exponents, which states that: \(a^{m} \cdot a^{n} = a^{m+n}\), where \(a\) is the common base, \(m\) is the exponent of first term and \(n\) is the exponent of second term.
02

Add the exponents

Applying the product of powers law on \(2^{2} \cdot 2^{3}\) will combine the expression into a single expression with the base 2 and the addition of the exponents 2 and 3, i.e., \(2^{2+3}\).
03

Calculate the exponent

Calculation of 2+3 will give 5. Hence, the expression becomes \(2^{5}\).
04

Calculate the power

Now calculate 2 to the power of 5 i.e, \(2 * 2* 2 * 2 * 2\) which is equal to 32.

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