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Chapter 1: Problem 54

Evaluate each expression. $$(6.7-9.88)^{3}$$

Short Answer

Expert verified
-32.144232

Step by step solution

01

Subtract the Numbers

Start by subtracting 9.88 from 6.7. Formula: \(6.7 - 9.88\)
02

Calculate the Difference

Perform the subtraction: \(6.7 - 9.88 = -3.18\)
03

Cube the Result

Now, cube the result of the subtraction: \((-3.18)^{3}\)
04

Compute the Cubic Value

Calculate the cube of -3.18: \((-3.18)^{3} = -32.144232\)

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

subtraction
Subtraction is one of the basic operations in arithmetic. It's the process of finding the difference between two numbers. To subtract, you take one number away from another. For example, in the expression, \(6.7 - 9.88\), you are subtracting 9.88 from 6.7.
To perform this, align the decimal points and subtract from right to left:
    \t
  • First, subtract the hundredths place: 0.70 - 0.88 (which involves borrowing because 0.88 is larger).
    • \t
  • Second, subtract the units place: 6 - 9 (again, you need to borrow).

Keep in mind, if the number being subtracted is larger, the result will be negative as seen here, \(6.7 - 9.88 = -3.18\).
cube of a number
Cubing a number means multiplying that number by itself three times. For example, the cube of \(3\) is \(3 \times 3 \times 3 = 27\).
In our exercise, we found the result of the subtraction to be \(-3.18\). To find the cube of \(-3.18\), multiply it by itself three times:
    \t
  • First multiplication: \(-3.18 \times -3.18 = 10.1124\)
    • \t
  • Second multiplication: \(10.1124 \times -3.18 = -32.144232\)

Notice how the negative sign affects the cubing process. Because one of the multiplications involves a negative number, the final result is also negative: \((-3.18)^{3} = -32.144232\).
negative numbers in algebra
Negative numbers are numbers less than zero and are vital in algebra. When dealing with negative numbers, you must be mindful of the rules:
    \t
  • Adding a negative number is the same as subtraction: \(a + (-b) = a - b\)
    • \t
  • Multiplying two negative numbers results in a positive number.
    • \t
  • Multiplying a positive and a negative number results in a negative number.

When we calculated \((-3.18)^{3}\), we were reminded of these rules. The multiplication steps involved:
    \t
  • First multiplication: \(-3.18 \times -3.18\) gave a positive number.
    • \t
  • Second multiplication: \(10.1124 \times -3.18\) resulted in a negative number because a positive and a negative number were multiplied.

Understanding how to manipulate negative numbers in equations helps solve algebraic expressions correctly.

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Most popular questions from this chapter

Simplify each expression. $$ t^{2}-5 w-\left(-2 w-t^{2}\right) $$

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Simplify each expression. $$ -7\left(x^{2}-x-1\right)+3\left(2 x^{2}-4 x+2\right) $$

Combine like terms. $$ 2 b^{2} x-16 b^{2} x $$

Solve each problem. Cooperative learning The sum of the integers from 1 through \(n\) is \(\frac{n(n+1)}{2}\) The sum of the squares of the integers from 1 through \(n\) is \(\frac{n(n+1)(2 n+1)}{6} .\) The sum of the cubes of the integers from 1 through \(n\) is \(\frac{n^{2}(n+1)^{2}}{4} .\) Use the appropriate expressions to find the following values. a) The sum of the integers from 1 through 50 b) The sum of the squares of the integers from 1 through 40 c) The sum of the cubes of the integers from 1 through 30 d) The square of the sum of the integers from 1 through 20 e) The cube of the sum of the integers from 1 through 10
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