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Chapter 3: Problem 2

Perform the following calculations. Check the results using your calculator. a. \((-2)(-4)(1)(-5)\) b. ( 3)\((-4)(2)(-4)(2)\) c. \((-1)(-1)(-1)(-1)\) d. \((-1)(-5)(-11)\) e. \(-6^{2}\) f. \((-6)^{2}\) g. \((-4)^{3}\) h. \(-4^{3}\)

Short Answer

Expert verified
Question: Solve the following exercises and check your results with a calculator. a. \((-2)(-4)(1)(-5)\) b. \((3)(-4)(2)(-4)(2)\) c. \((-1)(-1)(-1)(-1)\) d. \((-1)(-5)(-11)\) e. \(-6^{2}\) f. \((-6)^{2}\) g. \((-4)^{3}\) h. \(-4^{3}\) Answer: a. -40 b. 192 c. 1 d. -55 e. 36 f. 36 g. -64 h. -64

Step by step solution

01

a. \((-2)(-4)(1)(-5)\)

We apply the properties of multiplication: \((a)(b) = ab\). 1. Multiply \((-2)(-4)\): Since the product of two negative numbers is positive, we have \((-2)(-4) = 8\) 2. Multiply \(8(1)\): Since any number multiplied by 1 remains the same, we have \(8(1)=8\) 3. Multiply \(8(-5)\): Since the product of a positive and a negative number is negative, we have \(8(-5)=-40\) The result is \(-40\). Double-check this with the calculator.
02

b. \((3)(-4)(2)(-4)(2)\)

Multiply the numbers consecutively: 1. Multiply \((3)(-4)\): Since the product of a positive and a negative number is negative, we have \((3)(-4) = -12\) 2. Multiply \((-12)(2)\): Since the product of a negative and a positive number is negative, we have \((-12)(2)=-24\) 3. Multiply \((-24)(-4)\): Since the product of two negative numbers is positive, we have \((-24)(-4)=96\) 4. Multiply \((96)(2)\): Since the product of two positive numbers is positive, we have \((96)(2)=192\) The result is \(192\). Double-check this with the calculator.
03

c. \((-1)(-1)(-1)(-1)\)

Multiply the numbers consecutively: 1. Multiply \((-1)(-1)\): Since the product of two negative numbers is positive, we have \((-1)(-1) = 1\) 2. Multiply \((1)(-1)\): Since the product of a positive and a negative number is negative, we have \((1)(-1)=-1\) 3. Multiply \((-1)(-1)\): Since the product of two negative numbers is positive, we have \((-1)(-1)=1\) The result is \(1\). Double-check this with the calculator.
04

d. \((-1)(-5)(-11)\)

Multiply the numbers consecutively: 1. Multiply \((-1)(-5)\): Since the product of two negative numbers is positive, we have \((-1)(-5)=5\) 2. Multiply \(5(-11)\): Since the product of a positive and a negative number is negative, we have \(5(-11)=-55\) The result is \(-55\). Double-check this with the calculator.
05

e. \(-6^{2}\)

We apply the exponentiation operation: 1. Compute \((-6)^{2}\): Since the square of a negative number is positive, we have \((-6)^{2}=36\) The result is \(36\). Double-check this with the calculator.
06

f. \((-6)^{2}\)

We apply the exponentiation operation: 1. Compute \((-6)^{2}\): Since the square of a negative number is positive, we have \((-6)^{2}=36\) The result is \(36\). Double-check this with the calculator.
07

g. \((-4)^{3}\)

We apply the exponentiation operation: 1. Compute \((-4)^{3}\): Since the cube of a negative number is negative, we have \((-4)^{3}=-64\) The result is \(-64\). Double-check this with the calculator.
08

h. \(-4^{3}\)

We apply the exponentiation operation: 1. Compute \(4^{3}\): Since the cube of \(4\) is \(64\), we have \(-4^{3}=-64\) The result is \(-64\). Double-check this with the calculator.

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Most popular questions from this chapter

Evaluate the following. Check your results by using your calculator. a. \(3+2 \cdot 4 \) b. \(3-2(-4) \) c. \(-2+(2 \cdot 4-3 \cdot 5)\) d. \(3^{2}-5\) e. \(-6^{2}\) f. \((-6)^{2}\) g. \((-2)^{2}+10 \div(-5)\) h. \(12-3^{2}\) i. \(-12 \div 3-4^{2}\) j. \((2 \cdot 3-4 \cdot 5) \div(-2)\) k. \((-13-5) \div 3 \cdot 2 \cdot 1\) l. \(-5+9 \div(8-11)\) m. \(14-(-4)^{2}\) n. \(3-2^{3}\) o. \(3^{2}(-5)^{2} \div(-1)\) j. \((2 \cdot 3-4 \cdot 5) \div(-2)\) k. \((-13-5) \div 3 \cdot 2 \cdot 1\)
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The sum of two integers is 3. a. Translate this verbal rule into an equation where \(x\) represents one integer and \(y\) the other. b. Use the equation in part a to complete the following table. (TABLE CANNOT COPY) c. Plot the values from the table in part b on an appropriately labeled and scaled coordinate system. (GRAPH CANNOT COPY) d. Connect the points on the graph to obtain a graphical representation of the equation in part a.
Problem Solving with Integers The temperature increased by \(8^{\circ} \mathrm{F}\) from $-10^{\circ} \mathrm{F}$. What is the new temperature?
a. Another way to write an equation expressing your change in weight during the first 2 weeks of your diet is to subtract the initial weight, \(154,\) from your final weight, \(149 .\) Then the equation is \(x=149-154,\) where \(x\) represents the change in weight. Determine the value of \(x .\) b. Write a formula to calculate the amount a quantity changes when you know the final value and the initial value. Use the words final value, initial value, and change in quantity to represent the variables in the formula. (Hint: Use the equation from part a as a guide.)
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