Solve 36/5*2.5^3/2!(2.5-1)

$$\frac { \frac { 36 } { 5 \times 2.5 ^ { 3 } } } { 2 ! } ( 2.5 - 1 )$$

Evaluate

$$0.3456$$

Solution Steps

Calculate 2.5 to the power of 3 and get 15.625.

$$\frac{\frac{36}{5\times 15.625}}{2!}\left(2.5-1\right)$$

Multiply 5 and 15.625 to get 78.125.

$$\frac{\frac{36}{78.125}}{2!}\left(2.5-1\right)$$

Expand \frac{36}{78.125} by multiplying both numerator and the denominator by 1000.

$$\frac{\frac{36000}{78125}}{2!}\left(2.5-1\right)$$

Reduce the fraction \frac{36000}{78125} to lowest terms by extracting and canceling out 125.

$$\frac{\frac{288}{625}}{2!}\left(2.5-1\right)$$

The factorial of 2 is 2.

$$\frac{\frac{288}{625}}{2}\left(2.5-1\right)$$

Express \frac{\frac{288}{625}}{2} as a single fraction.

$$\frac{288}{625\times 2}\left(2.5-1\right)$$

Multiply 625 and 2 to get 1250.

$$\frac{288}{1250}\left(2.5-1\right)$$

Reduce the fraction \frac{288}{1250} to lowest terms by extracting and canceling out 2.

$$\frac{144}{625}\left(2.5-1\right)$$

Subtract 1 from 2.5 to get 1.5.

$$\frac{144}{625}\times 1.5$$

Convert decimal number 1.5 to fraction \frac{15}{10}. Reduce the fraction \frac{15}{10} to lowest terms by extracting and canceling out 5.

$$\frac{144}{625}\times \frac{3}{2}$$

Multiply \frac{144}{625} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{144\times 3}{625\times 2}$$

Do the multiplications in the fraction \frac{144\times 3}{625\times 2}.

$$\frac{432}{1250}$$

Reduce the fraction \frac{432}{1250} to lowest terms by extracting and canceling out 2.

$$\frac{216}{625}$$

Factor

$$\frac{2 ^ {3} \cdot 3 ^ {3}}{5 ^ {4}} = 0.3456$$