Solve frac{{left({C}_{13}right)}^{7}{left({C}_{13}right)}^3{left({C}_{13}right)}^1{left({C}_{13}right)}^2{left({A}_{13}right)}^6}{4^13}

$$\frac{ { \left( { C }_{ 13 } \right) }^{ 7 } { \left( { C }_{ 13 } \right) }^{ 3 } { \left( { C }_{ 13 } \right) }^{ 1 } { \left( { C }_{ 13 } \right) }^{ 2 } { \left( { A }_{ 13 } \right) }^{ 6 } }{ { 4 }^{ 13 } }$$

Evaluate

$$\frac{A_{13}^{6}C_{13}^{13}}{67108864}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 7 and 3 to get 10.

$$\frac{C_{13}^{10}C_{13}^{1}C_{13}^{2}A_{13}^{6}}{4^{13}}$$

To multiply powers of the same base, add their exponents. Add 10 and 1 to get 11.

$$\frac{C_{13}^{11}C_{13}^{2}A_{13}^{6}}{4^{13}}$$

To multiply powers of the same base, add their exponents. Add 11 and 2 to get 13.

$$\frac{C_{13}^{13}A_{13}^{6}}{4^{13}}$$

Calculate 4 to the power of 13 and get 67108864.

$$\frac{C_{13}^{13}A_{13}^{6}}{67108864}$$

Differentiate w.r.t. A_13

$$\frac{3A_{13}^{5}C_{13}^{13}}{33554432}$$