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Chapter 0: Problem 17

Evaluate each exponential expression. $$\frac{2^{8}}{2^{4}}$$

Short Answer

Expert verified
The result of the simplification is 16.

Step by step solution

01

Identify the base and the exponent

The base in both terms is 2. The exponent in the numerator is 8 and in the denominator is 4.
02

Apply the division property of exponents

The division property of exponents states that \(a^{m} 梅 a^{n} = a^{m-n}\). So, \(\frac{2^{8}}{2^{4}} = 2^{8-4}\).
03

Subtract the exponents

Subtract the exponent in the denominator from the exponent in the numerator. Hence, \(2^{8-4} = 2^{4}\).
04

Calculate the result

Raising 2 to the power of 4 equals 16. Hence, \(2^{4} = 16\).

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Most popular questions from this chapter

$$\frac{5}{4} \cdot \frac{8}{15}$$

Evaluate each algebraic expression for the given value or values of the variable(s). $$\frac{2 x+3 y}{x+1}, \text { for } x=-2 \text { and } y=4$$

Evaluate each algebraic expression for the given value or values of the variable(s). $$x^{2}-4(x-y), \text { for } x=8 \text { and } y=3$$

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$$\text { Factor completely.}$$ $$(y+1)^{3}+1$$
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