Solve 32*(-3/2)^3+96*(3/2)^2+72*(3/2)+16quad+6

$$32 \times ( - \frac { 3 } { 2 } ) ^ { 3 } + 96 \times ( \frac { 3 } { 2 } ) ^ { 2 } + 72 \times ( \frac { 3 } { 2 } ) + 16 \quad + 6$$

Evaluate

$$238$$

Solution Steps

Calculate -\frac{3}{2} to the power of 3 and get -\frac{27}{8}.

$$32\left(-\frac{27}{8}\right)+96\times \left(\frac{3}{2}\right)^{2}+72\times \frac{3}{2}+16+6$$

Express 32\left(-\frac{27}{8}\right) as a single fraction.

$$\frac{32\left(-27\right)}{8}+96\times \left(\frac{3}{2}\right)^{2}+72\times \frac{3}{2}+16+6$$

Multiply 32 and -27 to get -864.

$$\frac{-864}{8}+96\times \left(\frac{3}{2}\right)^{2}+72\times \frac{3}{2}+16+6$$

Divide -864 by 8 to get -108.

$$-108+96\times \left(\frac{3}{2}\right)^{2}+72\times \frac{3}{2}+16+6$$

Calculate \frac{3}{2} to the power of 2 and get \frac{9}{4}.

$$-108+96\times \frac{9}{4}+72\times \frac{3}{2}+16+6$$

Express 96\times \frac{9}{4} as a single fraction.

$$-108+\frac{96\times 9}{4}+72\times \frac{3}{2}+16+6$$

Multiply 96 and 9 to get 864.

$$-108+\frac{864}{4}+72\times \frac{3}{2}+16+6$$

Divide 864 by 4 to get 216.

$$-108+216+72\times \frac{3}{2}+16+6$$

Add -108 and 216 to get 108.

$$108+72\times \frac{3}{2}+16+6$$

Express 72\times \frac{3}{2} as a single fraction.

$$108+\frac{72\times 3}{2}+16+6$$

Multiply 72 and 3 to get 216.

$$108+\frac{216}{2}+16+6$$

Divide 216 by 2 to get 108.

$$108+108+16+6$$

Add 108 and 108 to get 216.

$$216+16+6$$

Add 216 and 16 to get 232.

$$232+6$$

Add 232 and 6 to get 238.

$$238$$

Factor

$$2\times 7\times 17$$