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Chapter 0: Problem 122

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

Short Answer

Expert verified
The product of \(2^{3} \cdot 2^{5}\) equals to 256 when applying the product rule for exponents.

Step by step solution

01

Recognize the problem

Here we have a multiplication involving two power expressions with the same base: \(2^{3} \cdot 2^{5}\). Consider the product rule of exponents which states that when the same bases are multiplied, you add the exponents.
02

Applying the exponent product rule

According to the rule, \(2^{3} \cdot 2^{5}\) becomes \(2^{3+5}\).
03

Simplify the exponent

Simplify the exponent by adding it together. So, \(2^{3+5}\) becomes \(2^{8}\)
04

Compute the Power

Finally, calculate \(2^{8} = 256\).

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