$\frac{5+2(-8)}{(-2)^3-3}$
Answer (2)
Evaluate the numerator: 5 + 2 ( − 8 ) = − 11 .
Evaluate the denominator: ( − 2 ) 3 − 3 = − 8 − 3 = − 11 .
Divide the numerator by the denominator: − 11 − 11 = 1 .
The final answer is 1 .
Explanation
Understanding the Expression We are asked to evaluate the expression ( − 2 ) 3 − 3 5 + 2 ( − 8 ) . This involves evaluating the numerator and the denominator separately, and then dividing the numerator by the denominator.
Evaluating the Numerator First, let's evaluate the numerator: 5 + 2 ( − 8 ) = 5 − 16 = − 11 .
Evaluating the Denominator Next, let's evaluate the denominator: ( − 2 ) 3 − 3 = − 8 − 3 = − 11 .
Dividing Numerator by Denominator Now, we divide the numerator by the denominator: − 11 − 11 = 1 .
Final Answer Therefore, the value of the expression is 1.
Examples
In real-world scenarios, evaluating expressions like this is fundamental in various fields such as physics, engineering, and finance. For instance, if you're calculating the net force acting on an object, you might have to evaluate an expression similar to this to find the magnitude of the force. Similarly, in finance, you might use such expressions to calculate returns on investments or to determine the profitability of a project. Understanding how to simplify and evaluate these expressions is crucial for making informed decisions and solving complex problems.
We evaluated the expression ( − 2 ) 3 − 3 5 + 2 ( − 8 ) by calculating the numerator as − 11 and the denominator as − 11 , resulting in an overall value of 1 .
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