Question
Evaluate. \[ \left((-1)^{2}-4\right)^{3}+4 \cdot(-5) \]
Ask by Vaughan Simmons. in the United States
Feb 20,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The evaluated expression is -47.
Solution
First, compute (-1)², which is 1. Then the expression becomes:
(1 - 4)³ + 4 · (-5)
1 - 4 equals -3, so:
(-3)³ = -27
Next, 4 · (-5) is -20. Therefore, the overall expression is:
-27 + (-20) = -47
The evaluated expression is -47.
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Simplify this solution Beyond the Answer
To evaluate the expression \[ \left((-1)^{2}-4\right)^{3}+4 \cdot(-5), \] let's break it down step by step. First, calculate \((-1)^2\): \[ (-1)^2 = 1. \] Now substitute this back into the expression: \[ \left(1 - 4\right)^{3} + 4 \cdot (-5). \] Next, simplify \(1 - 4\): \[ 1 - 4 = -3. \] Now we have: \[ (-3)^{3} + 4 \cdot (-5). \] Now, calculate \((-3)^{3}\): \[ (-3)^{3} = -27. \] Next, compute \(4 \cdot (-5)\): \[ 4 \cdot (-5) = -20. \] Now we can substitute these values back into the expression: \[ -27 - 20. \] Finally, simplify \(-27 - 20\): \[ -27 - 20 = -47. \] Thus, the evaluated expression is: \[ \boxed{-47}. \]
