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Chapter 5: Problem 96

Use the order of operations to find the value of each expression. \(-3(-6+8)^{3}-5(-3+5)^{3}\)

Short Answer

Expert verified
The value of the expression \(-3(-6+8)^{3}-5(-3+5)^{3}\) is 16.

Step by step solution

01

Evaluate Expressions in Parentheses

First, calculate the value of the expressions within the parentheses. \nFor (-6+8) the result is 2, and for (-3+5) the result is 2 as well.
02

Apply Exponentiation

Next, apply the exponent of 3 to both 2 resulting from the first step.\n Thus, \(2^3\) equals 8.
03

Apply Multiplication

Multiply -3 by the above result for expression -3(2)^3, and -5 by the above result for expression -5(2)^3. This gives us -24 and -40 respectively.
04

Apply Subtraction

Now, subtract the second result from the first. That is, -24 - (-40). Be careful with double negatives, as subtracting a negative number is the same as adding a positive number, thus transforming the expression into -24 + 40.
05

Get The Final Result

The last step is to perform the addition operation, from step 4 we have -24 + 40, giving us 16.

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Most popular questions from this chapter

Write a formula for the general term (the nth term) of each arithmetic sequence. Then use the formula for \(a_{n}\) to find \(a_{20}\), the 20 th term of the sequence. \(1,5,9,13, \ldots\)

Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=2, r=0.1\)

Write a formula for the general term (the nth term) of each geometric sequence. Then use the formula for \(a_{n}\) to find \(a_{7}\), the seventh term of the sequence. \(0.0007,-0.007,0.07,-0.7, \ldots\)

Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(15,30,60,120, \ldots\)

Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=-\frac{1}{16}, r=-4\)
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