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Chapter 0: Problem 13

Evaluate the expressions. $$ 2^{3} 2^{2} $$

Short Answer

Expert verified
The final result of the given expression \(2^{3} * 2^{2}\) is \(32\).

Step by step solution

01

Recall the Rule for Multiplying Powers with the Same Base

When we have two powers with the same base being multiplied together, we simply add the exponents. So, if we have \(a^{m} * a^{n}\), the result is \(a^{m+n}\).
02

Apply the Rule to the Expression

Since we have \(2^{3} * 2^{2}\), we apply the rule that we discussed in step 1 and add the exponents together: \(2^{3+2}\).
03

Simplify the Expression

We can simplify the expression by performing the addition operation in the exponent: \(2^{5}\).
04

Calculate the Final Result

Now we just need to evaluate the expression \(2^{5}\), which equals \(2 * 2 * 2 * 2 * 2 = 32\). The final result of the given expression \(2^{3} * 2^{2}\) is \(32\).

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