Question
5 Which expression is equivalent to the one below? * \( 50+5^{3} \) A. \( 5^{2}+7 \) ( B. \( 3^{2} \cdot 11 \) C. \( 5^{2} \cdot 7 \) D. \( 3^{2}+11 \)
Ask by Reid O'Quinn. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The equivalent expression is \( 5^{2} \cdot 7 \), which is option C.
Solution
To determine which expression is equivalent to \( 50 + 5^{3} \), let's evaluate each option:
1. **Original Expression:**
\[
50 + 5^{3} = 50 + 125 = 175
\]
2. **Option A: \( 5^{2} + 7 \)**
\[
5^{2} + 7 = 25 + 7 = 32 \quad (\text{Not equal to } 175)
\]
3. **Option B: \( 3^{2} \cdot 11 \)**
\[
3^{2} \cdot 11 = 9 \cdot 11 = 99 \quad (\text{Not equal to } 175)
\]
4. **Option C: \( 5^{2} \cdot 7 \)**
\[
5^{2} \cdot 7 = 25 \cdot 7 = 175 \quad (\text{Equal to } 175)
\]
5. **Option D: \( 3^{2} + 11 \)**
\[
3^{2} + 11 = 9 + 11 = 20 \quad (\text{Not equal to } 175)
\]
**Conclusion:** The expression equivalent to \( 50 + 5^{3} \) is:
**C. \( 5^{2} \cdot 7 \)**
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
Let's simplify the original expression \( 50 + 5^{3} \). Since \( 5^{3} \) equals \( 125 \), we have \( 50 + 125 = 175 \). Now, evaluating the options: A. \( 5^{2} + 7 = 25 + 7 = 32 \) B. \( 3^{2} \cdot 11 = 9 \cdot 11 = 99 \) C. \( 5^{2} \cdot 7 = 25 \cdot 7 = 175 \) (Bingo!) D. \( 3^{2} + 11 = 9 + 11 = 20 \) Hence, the expression equivalent to \( 50 + 5^{3} \) is C: \( 5^{2} \cdot 7 \). Guess who scored extra points? You, for recognizing how to break it down! Remember, knowing how to simplify can turn math into a fun puzzle! And just when you thought math was all doom and gloom! Keep that in mind next time you're crunching numbers.
