Solve f(6)=7/8(6)^3-3/2(6)^2+3/2(6)-4

$$f ( 6 ) = \frac { 7 } { 8 } ( 6 ) ^ { 3 } - \frac { 3 } { 2 } ( 6 ) ^ { 2 } + \frac { 3 } { 2 } ( 6 ) - 4$$

Evaluate

$$140$$

Solution Steps

Calculate 6 to the power of 3 and get 216.

$$\frac{7}{8}\times 216-\frac{3}{2}\times 6^{2}+\frac{3}{2}\times 6-4$$

Express \frac{7}{8}\times 216 as a single fraction.

$$\frac{7\times 216}{8}-\frac{3}{2}\times 6^{2}+\frac{3}{2}\times 6-4$$

Multiply 7 and 216 to get 1512.

$$\frac{1512}{8}-\frac{3}{2}\times 6^{2}+\frac{3}{2}\times 6-4$$

Divide 1512 by 8 to get 189.

$$189-\frac{3}{2}\times 6^{2}+\frac{3}{2}\times 6-4$$

Calculate 6 to the power of 2 and get 36.

$$189-\frac{3}{2}\times 36+\frac{3}{2}\times 6-4$$

Express \frac{3}{2}\times 36 as a single fraction.

$$189-\frac{3\times 36}{2}+\frac{3}{2}\times 6-4$$

Multiply 3 and 36 to get 108.

$$189-\frac{108}{2}+\frac{3}{2}\times 6-4$$

Divide 108 by 2 to get 54.

$$189-54+\frac{3}{2}\times 6-4$$

Subtract 54 from 189 to get 135.

$$135+\frac{3}{2}\times 6-4$$

Express \frac{3}{2}\times 6 as a single fraction.

$$135+\frac{3\times 6}{2}-4$$

Multiply 3 and 6 to get 18.

$$135+\frac{18}{2}-4$$

Divide 18 by 2 to get 9.

$$135+9-4$$

Add 135 and 9 to get 144.

$$144-4$$

Subtract 4 from 144 to get 140.

$$140$$

Factor

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