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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

A merchant sells three different sizes of canned tomatoes. A large can costs the same as 5 medium cans or 7 small cans. If a customer purchases an equal number of small and large cans of tomatoes for the same amount of money needed to buy 200 medium cans, how many small cans does she purchase? a. 35 b. 45 c. 72 d. 199 e. 208

If \(6 k-5 l=27\) and \(3 l-2 k=-13\) and \(5 k-5 l=j,\) what is the value of \(j ?\)

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The original selling price of an item at a store is 40 percent more than the cost of the item to the retailer. If the retailer reduces the price of the item by 15 percent of the original selling price, then the difference between the reduced price and the cost of the item to the retailer is what percent of the cost of the item to the retailer?

If \(3^{3} \times 9^{12}=3^{\mathrm{x}},\) what is the value of \(x ?\)
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