Problem

\( \frac{(-7)^{3} \times 7^{8} \times(-49)^{2}}{7^{-4} \times\left(-7^{3}\right)^{5}} \)

Answer

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Answer

\( \frac{7^{15}}{7^{-4} \times 1 \times 7^{15}} \) = \( \frac{7^{15}}{7^{15 - 4}} \) = 7^4 = \boxed{2401}

Steps

Step 1 ：\( \frac{(-7)^{3} \times 7^{8} \times(-49)^{2}}{7^{-4} \times\left(-7^{3}\right)^{5}} \) = \( \frac{(-7)^{3} \times 7^{8} \times(-7)^{2 \times 2}}{7^{-4} \times\left(-1 \times 7^{3}\right)^{5}} \)

Step 2 ：\( \frac{(-7)^{3} \times 7^{8} \times(-7)^{4}}{7^{-4} \times(-1)^{5} \times 7^{15}} \) = \( \frac{7^{3 + 8 + 4}}{7^{-4} \times(-1)^{6} \times 7^{15}} \)

Step 3 ：\( \frac{7^{15}}{7^{-4} \times 1 \times 7^{15}} \) = \( \frac{7^{15}}{7^{15 - 4}} \) = 7^4 = \boxed{2401}

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