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Chapter 0: Problem 20

Evaluate each exponential expression. $$ 2^{-3} \cdot 2 $$

Short Answer

Expert verified
The answer to the expression \(2^{-3} \cdot 2\) is \(1/4\).

Step by step solution

01

Evaluate the Exponential Part

Start by calculating \(2^{-3}\). A negative exponent means we take the reciprocal of the base, so \(2^{-3}=1/2^3\). Now simplify \(2^3\) which gives us 8, so \(2^{-3}=1/8\).
02

Multiply by 2

Now, replace \(2^{-3}\) with \(1/8\) in the original problem, which gives us \(1/8 \cdot 2\). Multiply these numbers together to find the solution.
03

Calculate the Answer

Multiplying \(1/8\) and 2 gives a result of \(1/4\). This is the solution.

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Most popular questions from this chapter

Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$\frac{5}{4} \cdot \frac{8}{15}$$

Factor and simplify each algebraic expression. $$(4 x-1)^{\frac{1}{2}}-1(4 x-1)^{\frac{3}{2}}$$

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Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$ 4^{-2}<4^{-3} $$

Factor and simplify each algebraic expression. $$\left(x^{2}+4\right)^{\frac{1}{2}}+\left(x^{2}+4\right)^{\frac{7}{2}}$$
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