To simplify the expression \( \frac{125^3}{75^3} \) using the Quotient Rule of Integer Exponents, we can rewrite it as follows:
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First, identify the base and apply the Quotient Rule: \[ \frac{a^m}{b^m} = \left(\frac{a}{b}\right)^m \] So, we can rewrite: \[ \frac{125^3}{75^3} = \left(\frac{125}{75}\right)^3 \]
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Now, simplify the fraction: \[ \frac{125}{75} = \frac{125 \div 25}{75 \div 25} = \frac{5}{3} \]
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So we get: \[ \left(\frac{5}{3}\right)^3 = \frac{5^3}{3^3} = \frac{125}{27} \]
Hence, the simplified expression for \( \frac{125^3}{75^3} \) is \( \frac{125}{27} \).
From the options provided:
- 553
- \( 5^{53} \)
- \( 5^{106} \)
- \( 12^{106} \)
- \( 12^{53} \) divided by \( 7^{53} \)
It looks like none of these match our simplified expression of \( \frac{125}{27} \). Please verify if there's any additional context or constraints that might change the evaluation.
1 answer