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2) \( \frac{7^{2} \times 5^{3}}{5^{2}}= \)

Ask by Burgess Chen. in South Africa
Feb 20,2025

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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: \(245\)

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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! 🕺💡

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