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Chapter 0: Problem 100

Explain the product rule for exponents. Use \(2^{3} \cdot 2^{5}\) in your explanation.

Short Answer

Expert verified
The result of \(2^{3} \cdot 2^{5}\) according to the product rule for exponents is \(2^{8}\)

Step by step solution

01

Understand the Product Rule for Exponents

The product rule for exponents states that, for any numbers \(a\), \(m\), and \(n\), \(a^{m} \cdot a^{n} = a^{m+n}\). This means if you are multiplying two expressions that have the same base, you can simply add the exponents.
02

Apply the Product Rule to Given Problem

In the given problem, we have \(2^{3} \cdot 2^{5}\). According to the product rule, this can be simplified by adding the exponents since the bases (which are 2 in both terms) are the same. So it can be rewritten as: \(2^{(3+5)}\)
03

Calculate

Perform the addition in the exponent: \(2^{8}\)

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