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Chapter 5: Problem 105

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

Short Answer

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

Step by step solution

01

Identify the Base and Exponents

In the given example \(2^{3} \cdot 2^{5}\), the base is \(2\) and the exponents are \(3\) and \(5\) respectively.
02

Apply the Product Rule for Exponents

According to the product rule for exponents - when multiplying like bases, add the exponents. So, \(2^{3} \cdot 2^{5} = 2^{3+5}\).
03

Simplify the result

Add the exponents: \(2^{3+5} = 2^{8}\).

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Most popular questions from this chapter

Perform the indicated operations. $$(x+4)(x-5)-(x+3)(x-6)$$

Explain how to simplify an expression that involves a quotient raised to a power. Provide an example with your explanation.

Explain the difference between performing these two operations: $$2 x^{2}+3 x^{2} \text { and }\left(2 x^{2}\right)\left(3 x^{2}\right)$$

In each exercise, find the product. $$4 x^{3}\left(4 x^{2}-3 x+1\right)$$

Will help you prepare for the material covered in the next section. In each exercise, find the indicated products. Then, if possible, state a fast method for finding these products. (You may already be familiar with some of these methods from a high school algebra course.) a. \((x+3)(x+4)\) b. \((x+5)(x+20)\)
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