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Chapter 5: Problem 108

Use the order of operations to find the value of each expression. \(\left[-4^{2}+(7-10)^{3}-(-27)\right]-\left[|-2|^{5}+1-5^{2}\right]\)

Short Answer

Expert verified
The value of the given expression is -24.

Step by step solution

01

Perform the operations inside the brackets

Here we have two types of operations inside brackets: power and subtraction. According to the order of operations, power should be carried out before addition and subtraction. \n So, for the first bracket, \n \( -4^{2} = -16 \), \n \( (7-10)^{3} = -3^{3} = -27 \), \n \( |-2|^{5} = 2^{5} = 32 \). \n Hence the first bracket becomes: \n \( -16 + (-27) - (-27) = -16 - 27 + 27 \). \n The second bracket becomes: \n \( 32 + 1 - 5^{2} = 32 + 1 - 25 \).
02

Perform the additions and subtractions inside the brackets

Now, we can simplify the operations with addition and subtraction in both brackets: \n The first bracket simplifies to: \n \( -16 - 27 + 27 = -16 \). \n The second bracket simplifies to: \n \( 32 + 1 - 25 = 8 \). \n So, the full equation becomes: \n \( -16 - 8 \).
03

calculate the final result

Finally, the value of the full equation, \( -16 - 8 = -24 \).

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