Solve A_3^3*A_3^3*A_3^3*6/A_9^9

$$\frac { A _ { 3 } ^ { 3 } \times A _ { 3 } ^ { 3 } \times A _ { 3 } ^ { 3 } \times 6 } { A _ { 9 } ^ { 9 } }$$

Evaluate

$$6\times \left(\frac{A_{3}}{A_{9}}\right)^{9}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$\frac{A_{3}^{6}A_{3}^{3}\times 6}{A_{9}^{9}}$$

To multiply powers of the same base, add their exponents. Add 6 and 3 to get 9.

$$\frac{A_{3}^{9}\times 6}{A_{9}^{9}}$$

Differentiate w.r.t. A_9

$$-\frac{54A_{3}^{9}}{A_{9}^{10}}$$