Question
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Tutor-Verified Answer
Answer
\( \frac{7^{2} \times 5^{3}}{5^{2}} = 49 \times 125 / 25 = 6125 / 25 = 245 \)
Solution
Calculate or simplify the expression \( (7^2 * 5^3) / (5^2) \).
Calculate the value by following steps:
- step0: Calculate:
\(\frac{\left(7^{2}\times 5^{3}\right)}{5^{2}}\)
- step1: Remove the parentheses:
\(\frac{7^{2}\times 5^{3}}{5^{2}}\)
- step2: Multiply by \(a^{-n}:\)
\(7^{2}\times 5^{3}\times 5^{-2}\)
- step3: Multiply the terms:
\(7^{2}\times 5^{3-2}\)
- step4: Subtract the numbers:
\(7^{2}\times 5\)
- step5: Evaluate the power:
\(49\times 5\)
- step6: Multiply:
\(245\)
Answered by UpStudy AI and reviewed by a Professional Tutor
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Bonus Knowledge
To simplify the expression \( \frac{7^{2} \times 5^{3}}{5^{2}} \), you can start by applying the properties of exponents. Since you're dividing, you subtract the exponents of the same base. Thus, \( 5^{3} / 5^{2} = 5^{3-2} = 5^{1} \). Now, combining this with \( 7^{2} \), you get \( 7^{2} \times 5^{1} = 49 \times 5 = 245 \). So, the final answer is \( 245 \). And voila! You’ve navigated the world of exponents with style—who knew math could be this straightforward? Just remember: when you're dividing with like bases, it's all about that exponent subtraction game! 🕺💡