Question

simplifique a expressão 6!.7!/9!.3!​

Answer 1

$\cfrac{6! \cdot 7!}{9! \cdot 3!} \\\\= \cfrac{6 \cdot 5 \cdot 4 \cdot 3! \cdot 7!}{9 \cdot 8 \cdot 7! \cdot 3!}\\\\= \cfrac{6 \cdot 5 \cdot 4}{9 \cdot 8} \\\\= \cfrac{6 \cdot 5 \cdot 4}{3 \cdot 3 \cdot 2 \cdot 2 \cdot 2} \\\\= \cfrac{6 \cdot 5 \cdot 4}{6 \cdot 3 \cdot 4} \\\\= \cfrac{5}{3}$

5/3

Answer 2

$\LARGE\tt{} 6! \times \dfrac{7!}{9!} \times 3! \\ \\ \\ \LARGE\tt{}6! \times \frac{7!}{9 \times 8 \times7! } \times 3! \\ \\ \\ \LARGE\tt{}6! \times \dfrac{\cancel{7!}}{9 \times 8 \times\cancel{7!} } \\ \\ \\ \LARGE\tt{}6! \times \dfrac{1}{9 \times 8} \times 3! \\ \\ \\ \LARGE\tt{}6 \times \dfrac{1}{72} \times 3\LARGE\tt{} 6! \times \dfrac{7!}{9!} \times 3! \\ \\ \\ \LARGE\tt{}6! \times \frac{7!}{9 \times 8 \times7! } \times 3! \\ \\ \\ \LARGE\tt{}6! \times \dfrac{\cancel{7!}}{9 \times 8 \times\cancel{7!} } \\ \\ \\ \LARGE\tt{}6! \times \dfrac{1}{9 \times 8} \times 3! \\ \\ \LARGE\tt{}6! \times \dfrac{1}{72} \times 3! \\ \\ \LARGE\tt{} \frac{6! \times 3!}{72} \\ \\ \LARGE\tt{} \dfrac{6! \times 6}{72} \\ \\ \LARGE\tt{} \frac{6! \times \cancel{6}}{\cancel{72}} \\ \\ \\ \LARGE\tt{} \dfrac{6!}{12} \\ \\ \LARGE\tt{} \dfrac{720}{12} \\ \\ \LARGE\tt{} \dfrac{\cancel{720}}{\cancel{12}} \div 12 \\ \\ {\large\boxed{\boxed{  { \LARGE \tt 60 }}}}$

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