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Chapter 11: Problem 8

$$\begin{array}{cc}\text { Quantity } \mathbf{A} & \text { Quantity } \mathbf{B} \\ \frac{2^{-4}}{4^{-2}} & \frac{\sqrt{64}}{-2^{3}} \end{array}$$ a. Quantity A is greater b. Quantity B is greater. c. The two quantities are equal. d. The relationship cannot be determined from the information given.

Short Answer

Expert verified
a. Quantity A is greater

Step by step solution

01

Simplification of Quantity A

Quantity A is a fraction consisting of \(2^{-4}\) in the numerator and \(4^{-2}\) in the denominator. It simplifies as such: \[\frac{2^{-4}}{4^{-2}} = \frac{\frac{1}{2^4}}{\frac{1}{4^2}}\] By applying the rule for dividing fractions (i.e., multiply by the reciprocal), you can further simplify this to: \[\frac{1}{2^4} \times \frac{4^2}{1} = \frac{4^2}{2^4} = \frac{16}{16} = 1\]
02

Simplification of Quantity B

Quantity B consists of \(\sqrt{64}\) divided by \(-2^3\). Simplified, this looks like: \[\frac{\sqrt{64}}{-2^{3}} = \frac{8}{-8} = -1\]
03

Comparison of Quantities A and B

Now that we have simplified both quantities, we can compare them. Quantity A equals 1 and Quantity B equals -1. Thus, Quantity A is greater than Quantity B.

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Most popular questions from this chapter

If \(x=3 a\) and \(y=9 b,\) then all of the following are equal to \(2(x+y)\) EXCEPT a. \(3(2 a+6 b)\) b. \(6(a+3 b)\) c. \(24\left(\frac{1}{4} a+\frac{3}{4} b\right)\) d. \(\frac{1}{3}(18 a+54 b)\) e. \(12\left(\frac{1}{2} a+\frac{3}{4} b\right)\)

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