Solve (5*8^2-1/3*8^3)-(5*1^2-1/3*1^3)

$$( 5 \cdot 8 ^ { 2 } - \frac { 1 } { 3 } \cdot 8 ^ { 3 } ) - ( 5 \cdot 1 ^ { 2 } - \frac { 1 } { 3 } \cdot 1 ^ { 3 } )$$

Evaluate

$$\frac{434}{3}\approx 144.666666667$$

Solution Steps

Calculate 8 to the power of 2 and get 64.

$$5\times 64-\frac{1}{3}\times 8^{3}-\left(5\times 1^{2}-\frac{1}{3}\times 1^{3}\right)$$

Multiply 5 and 64 to get 320.

$$320-\frac{1}{3}\times 8^{3}-\left(5\times 1^{2}-\frac{1}{3}\times 1^{3}\right)$$

Calculate 8 to the power of 3 and get 512.

$$320-\frac{1}{3}\times 512-\left(5\times 1^{2}-\frac{1}{3}\times 1^{3}\right)$$

Multiply \frac{1}{3} and 512 to get \frac{512}{3}.

$$320-\frac{512}{3}-\left(5\times 1^{2}-\frac{1}{3}\times 1^{3}\right)$$

Convert 320 to fraction \frac{960}{3}.

$$\frac{960}{3}-\frac{512}{3}-\left(5\times 1^{2}-\frac{1}{3}\times 1^{3}\right)$$

Since \frac{960}{3} and \frac{512}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{960-512}{3}-\left(5\times 1^{2}-\frac{1}{3}\times 1^{3}\right)$$

Subtract 512 from 960 to get 448.

$$\frac{448}{3}-\left(5\times 1^{2}-\frac{1}{3}\times 1^{3}\right)$$

Calculate 1 to the power of 2 and get 1.

$$\frac{448}{3}-\left(5\times 1-\frac{1}{3}\times 1^{3}\right)$$

Multiply 5 and 1 to get 5.

$$\frac{448}{3}-\left(5-\frac{1}{3}\times 1^{3}\right)$$

Calculate 1 to the power of 3 and get 1.

$$\frac{448}{3}-\left(5-\frac{1}{3}\times 1\right)$$

Multiply \frac{1}{3} and 1 to get \frac{1}{3}.

$$\frac{448}{3}-\left(5-\frac{1}{3}\right)$$

Convert 5 to fraction \frac{15}{3}.

$$\frac{448}{3}-\left(\frac{15}{3}-\frac{1}{3}\right)$$

Since \frac{15}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{448}{3}-\frac{15-1}{3}$$

Subtract 1 from 15 to get 14.

$$\frac{448}{3}-\frac{14}{3}$$

Since \frac{448}{3} and \frac{14}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{448-14}{3}$$

Subtract 14 from 448 to get 434.

$$\frac{434}{3}$$

Factor

$$\frac{2 \cdot 7 \cdot 31}{3} = 144\frac{2}{3} = 144.66666666666666$$