Question
Follow the proper order of operations to evaluate the following. \( \frac{-7\left(5^{2}-20\right)}{9-14} \)
Ask by Page Love. in the United States
Jan 27,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The result of the expression is 7.
Solution
Certainly! Let's evaluate the expression step by step using the proper order of operations (PEMDAS/BODMAS):
\[
\frac{-7\left(5^{2}-20\right)}{9-14}
\]
### Step 1: Parentheses
First, evaluate the expressions inside the parentheses.
1. **Exponentiation inside the numerator:**
\[
5^{2} = 25
\]
2. **Subtract within the numerator's parentheses:**
\[
25 - 20 = 5
\]
3. **Subtract within the denominator:**
\[
9 - 14 = -5
\]
Now, the expression simplifies to:
\[
\frac{-7 \times 5}{-5}
\]
### Step 2: Multiplication
Multiply \(-7\) by \(5\):
\[
-7 \times 5 = -35
\]
Now, the expression is:
\[
\frac{-35}{-5}
\]
### Step 3: Division
Divide \(-35\) by \(-5\):
\[
\frac{-35}{-5} = 7
\]
### Final Answer
\[
7
\]
Reviewed and approved by the UpStudy tutoring team
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Explain 
Simplify this solution Beyond the Answer
First, let's simplify the expression step-by-step using the order of operations (PEMDAS/BODMAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). Start with the expression inside the parentheses: \(5^2 - 20\), which equals \(25 - 20 = 5\). Next, substitute this back into the equation: \(-7(5)\) gives \(-35\). Now, focus on the denominator: \(9 - 14 = -5\). So the main expression now looks like \(\frac{-35}{-5}\). Finally, dividing \(-35\) by \(-5\) gives you \(7\). Thus, the final result is \(7\).
