To simplify \( \frac{243^3}{5} \), we will first calculate \( 243^3 \) and then divide that result by 5.
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Calculate \( 243^3 \): \[ 243 = 3^5 \quad \text{(because \( 3^5 = 243 \))} \] Therefore, \[ 243^3 = (3^5)^3 = 3^{5 \cdot 3} = 3^{15} \]
Thus, \[ 243^3 = 3^{15} \]
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Now we have: \[ \frac{243^3}{5} = \frac{3^{15}}{5} \]
This is the simplified form. The expression \( \frac{3^{15}}{5} \) cannot be simplified further since there are no common factors between \( 3^{15} \) and \( 5 \).
Therefore, the final answer is: \[ \frac{3^{15}}{5} \]