Solve F=frac{15^{6}*12^{4}*5^{9}*6^3}{10^11*3^13*5^4}

$$F = \frac { 15 ^ { 6 } \times 12 ^ { 4 } \times 5 ^ { 9 } \times 6 ^ { 3 } } { 10 ^ { 11 } \times 3 ^ { 13 } \times 5 ^ { 4 } }$$

Solve for F

$$F=1$$

Steps for Solving Linear Equation

Cancel out 5^{4} in both numerator and denominator.

$$F=\frac{5^{5}\times 6^{3}\times 12^{4}\times 15^{6}}{3^{13}\times 10^{11}}$$

Calculate 5 to the power of 5 and get 3125.

$$F=\frac{3125\times 6^{3}\times 12^{4}\times 15^{6}}{3^{13}\times 10^{11}}$$

Calculate 6 to the power of 3 and get 216.

$$F=\frac{3125\times 216\times 12^{4}\times 15^{6}}{3^{13}\times 10^{11}}$$

Multiply 3125 and 216 to get 675000.

$$F=\frac{675000\times 12^{4}\times 15^{6}}{3^{13}\times 10^{11}}$$

Calculate 12 to the power of 4 and get 20736.

$$F=\frac{675000\times 20736\times 15^{6}}{3^{13}\times 10^{11}}$$

Multiply 675000 and 20736 to get 13996800000.

$$F=\frac{13996800000\times 15^{6}}{3^{13}\times 10^{11}}$$

Calculate 15 to the power of 6 and get 11390625.

$$F=\frac{13996800000\times 11390625}{3^{13}\times 10^{11}}$$

Multiply 13996800000 and 11390625 to get 159432300000000000.

$$F=\frac{159432300000000000}{3^{13}\times 10^{11}}$$

Calculate 3 to the power of 13 and get 1594323.

$$F=\frac{159432300000000000}{1594323\times 10^{11}}$$

Calculate 10 to the power of 11 and get 100000000000.

$$F=\frac{159432300000000000}{1594323\times 100000000000}$$

Multiply 1594323 and 100000000000 to get 159432300000000000.

$$F=\frac{159432300000000000}{159432300000000000}$$

Divide 159432300000000000 by 159432300000000000 to get 1.

$$F=1$$

Assign F

$$F≔1$$