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Chapter 5: Problem 107

Use the order of operations to find the value of each expression. \(\left[-5^{2}+(6-8)^{3}-(-4)\right]-\left[|-2|^{3}+1-3^{2}\right]\)

Short Answer

Expert verified
The result of the expression is -29.

Step by step solution

01

Calculate the Operations in the First Bracket

The operations in the first bracket are \(-5^{2}+(6-8)^{3}-(-4)\). Following the order of operations, the calculation should proceed as follows: a) \(6-8 = -2\); b) \(-2^{3} = -8\); c) \(-5^{2} = -25\) (since \(-5^{2}\) correlates to \(-1*5^{2}\)); d) \(-(-4) = 4\). Finally, add up the results: \(-25 - 8 + 4 = -29\)
02

Calculate the Operations in the Second Bracket

The operations in the second bracket are \(|-2|^{3}+1-3^{2}\). Following the order of operations, the calculation should proceed as follows: a) \(|-2| = 2\) (since the absolute value of -2 is 2); b) \(2^{3} = 8\); c) \(3^{2} = 9\); Finally, combine the results: \(8 + 1 - 9 = 0\)
03

Subtract the Result of Second Bracket from First

Now, subtract the result of the second bracket from the result of the first bracket which is \(-29 - 0 = -29\)

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Most popular questions from this chapter

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