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Chapter 5: Problem 95

Use the order of operations to find the value of each expression. \(6(3-5)^{3}-2(1-3)^{3}\)

Short Answer

Expert verified
The simplified value of the expression \(6(3-5)^{3}-2(1-3)^{3}\) is -32.

Step by step solution

01

Solve Inside Parentheses

According to the order of operations, first solve the expressions inside the parentheses. So, \(3-5=-2\) and \(1-3=-2\).
02

Apply Exponents

Next, according to the order of operations, solve the exponents. So, \((-2)^{3}=-8\) and \((-2)^{3}=-8\).
03

Perform Multiplication

Now, perform the multiplication in the expression. So, \(6 \times -8 = -48\) and \(2 \times -8 = -16\).
04

Perform Subtraction

Finally, subtract the two resulting values. So, \(-48 - (-16) = -48 + 16 = -32\).

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Most popular questions from this chapter

Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(3,8,13,18, \ldots\)

Find the indicated term for the geometric sequence with first term, \(a_{1}\), and common ratio, \(r\). Find \(a_{7}\), when \(a_{1}=5, r=-2\).

Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(2,6,10,14, \ldots\)

Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=4, r=2\)

Use the appropriate formula shown above to find \(2+4+6+8+\cdots+200\), the sum of the first 100 positive even integers.
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