Solve 50*150^3/12+(100*25^3/12+(2500)*(37.5)^3)*2

$$\frac { 50 \times 150 ^ { 3 } } { 12 } + ( \frac { 100 \times 25 ^ { 3 } } { 12 } + ( 2500 ) \times ( 37.5 ) ^ { 3 } ) \times 2$$

Evaluate

$$\frac{833984375}{3}\approx 277994791.666666667$$

Solution Steps

Calculate 150 to the power of 3 and get 3375000.

$$\frac{50\times 3375000}{12}+\left(\frac{100\times 25^{3}}{12}+2500\times 37.5^{3}\right)\times 2$$

Multiply 50 and 3375000 to get 168750000.

$$\frac{168750000}{12}+\left(\frac{100\times 25^{3}}{12}+2500\times 37.5^{3}\right)\times 2$$

Divide 168750000 by 12 to get 14062500.

$$14062500+\left(\frac{100\times 25^{3}}{12}+2500\times 37.5^{3}\right)\times 2$$

Calculate 25 to the power of 3 and get 15625.

$$14062500+\left(\frac{100\times 15625}{12}+2500\times 37.5^{3}\right)\times 2$$

Multiply 100 and 15625 to get 1562500.

$$14062500+\left(\frac{1562500}{12}+2500\times 37.5^{3}\right)\times 2$$

Reduce the fraction \frac{1562500}{12} to lowest terms by extracting and canceling out 4.

$$14062500+\left(\frac{390625}{3}+2500\times 37.5^{3}\right)\times 2$$

Calculate 37.5 to the power of 3 and get 52734.375.

$$14062500+\left(\frac{390625}{3}+2500\times 52734.375\right)\times 2$$

Multiply 2500 and 52734.375 to get 131835937.5.

$$14062500+\left(\frac{390625}{3}+131835937.5\right)\times 2$$

Convert decimal number 131835937.5 to fraction \frac{1318359375}{10}. Reduce the fraction \frac{1318359375}{10} to lowest terms by extracting and canceling out 5.

$$14062500+\left(\frac{390625}{3}+\frac{263671875}{2}\right)\times 2$$

Least common multiple of 3 and 2 is 6. Convert \frac{390625}{3} and \frac{263671875}{2} to fractions with denominator 6.

$$14062500+\left(\frac{781250}{6}+\frac{791015625}{6}\right)\times 2$$

Since \frac{781250}{6} and \frac{791015625}{6} have the same denominator, add them by adding their numerators.

$$14062500+\frac{781250+791015625}{6}\times 2$$

Add 781250 and 791015625 to get 791796875.

$$14062500+\frac{791796875}{6}\times 2$$

Express \frac{791796875}{6}\times 2 as a single fraction.

$$14062500+\frac{791796875\times 2}{6}$$

Multiply 791796875 and 2 to get 1583593750.

$$14062500+\frac{1583593750}{6}$$

Reduce the fraction \frac{1583593750}{6} to lowest terms by extracting and canceling out 2.

$$14062500+\frac{791796875}{3}$$

Convert 14062500 to fraction \frac{42187500}{3}.

$$\frac{42187500}{3}+\frac{791796875}{3}$$

Since \frac{42187500}{3} and \frac{791796875}{3} have the same denominator, add them by adding their numerators.

$$\frac{42187500+791796875}{3}$$

Add 42187500 and 791796875 to get 833984375.

$$\frac{833984375}{3}$$

Factor

$$\frac{7 \cdot 61 \cdot 5 ^ {9}}{3} = 277994791\frac{2}{3} = 277994791.6666667$$