Solve 4/3(-4)^3-4(-4)^2-96(-4)+17

$$\frac { 4 } { 3 } ( - 4 ) ^ { 3 } - 4 ( - 4 ) ^ { 2 } - 96 ( - 4 ) + 17$$

Evaluate

$$\frac{755}{3}\approx 251.666666667$$

Solution Steps

Calculate -4 to the power of 3 and get -64.

$$\frac{4}{3}\left(-64\right)-4\left(-4\right)^{2}-96\left(-4\right)+17$$

Express \frac{4}{3}\left(-64\right) as a single fraction.

$$\frac{4\left(-64\right)}{3}-4\left(-4\right)^{2}-96\left(-4\right)+17$$

Multiply 4 and -64 to get -256.

$$\frac{-256}{3}-4\left(-4\right)^{2}-96\left(-4\right)+17$$

Fraction \frac{-256}{3} can be rewritten as -\frac{256}{3} by extracting the negative sign.

$$-\frac{256}{3}-4\left(-4\right)^{2}-96\left(-4\right)+17$$

Calculate -4 to the power of 2 and get 16.

$$-\frac{256}{3}-4\times 16-96\left(-4\right)+17$$

Multiply 4 and 16 to get 64.

$$-\frac{256}{3}-64-96\left(-4\right)+17$$

Convert 64 to fraction \frac{192}{3}.

$$-\frac{256}{3}-\frac{192}{3}-96\left(-4\right)+17$$

Since -\frac{256}{3} and \frac{192}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-256-192}{3}-96\left(-4\right)+17$$

Subtract 192 from -256 to get -448.

$$-\frac{448}{3}-96\left(-4\right)+17$$

Multiply 96 and -4 to get -384.

$$-\frac{448}{3}-\left(-384\right)+17$$

The opposite of -384 is 384.

$$-\frac{448}{3}+384+17$$

Convert 384 to fraction \frac{1152}{3}.

$$-\frac{448}{3}+\frac{1152}{3}+17$$

Since -\frac{448}{3} and \frac{1152}{3} have the same denominator, add them by adding their numerators.

$$\frac{-448+1152}{3}+17$$

Add -448 and 1152 to get 704.

$$\frac{704}{3}+17$$

Convert 17 to fraction \frac{51}{3}.

$$\frac{704}{3}+\frac{51}{3}$$

Since \frac{704}{3} and \frac{51}{3} have the same denominator, add them by adding their numerators.

$$\frac{704+51}{3}$$

Add 704 and 51 to get 755.

$$\frac{755}{3}$$

Factor

$$\frac{5 \cdot 151}{3} = 251\frac{2}{3} = 251.66666666666666$$