Solve 7!*8*7/2!2!2!

$$\frac { 7 ! \times 8 \times 7 } { 2 ! 2 ! 2 ! }$$

Evaluate

$$35280$$

Solution Steps

Multiply 2! and 2! to get \left(2!\right)^{2}.

$$\frac{7!\times 8\times 7}{\left(2!\right)^{2}\times 2!}$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{7!\times 8\times 7}{\left(2!\right)^{3}}$$

The factorial of 7 is 5040.

$$\frac{5040\times 8\times 7}{\left(2!\right)^{3}}$$

Multiply 5040 and 8 to get 40320.

$$\frac{40320\times 7}{\left(2!\right)^{3}}$$

Multiply 40320 and 7 to get 282240.

$$\frac{282240}{\left(2!\right)^{3}}$$

The factorial of 2 is 2.

$$\frac{282240}{2^{3}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{282240}{8}$$

Divide 282240 by 8 to get 35280.

$$35280$$

Factor

$$2^{4}\times 3^{2}\times 5\times 7^{2}$$