Solve 8^3/12-(4*8^2)+(48*8)+0.05

$$\frac{ { 8 }^{ 3 } }{ 12 } -(4 \times { 8 }^{ 2 } )+(48 \times 8)+0.05$$

Evaluate

$$\frac{10243}{60}\approx 170.716666667$$

Solution Steps

Calculate 8 to the power of 3 and get 512.

$$\frac{512}{12}-4\times 8^{2}+48\times 8+0.05$$

Reduce the fraction \frac{512}{12} to lowest terms by extracting and canceling out 4.

$$\frac{128}{3}-4\times 8^{2}+48\times 8+0.05$$

Calculate 8 to the power of 2 and get 64.

$$\frac{128}{3}-4\times 64+48\times 8+0.05$$

Multiply 4 and 64 to get 256.

$$\frac{128}{3}-256+48\times 8+0.05$$

Convert 256 to fraction \frac{768}{3}.

$$\frac{128}{3}-\frac{768}{3}+48\times 8+0.05$$

Since \frac{128}{3} and \frac{768}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{128-768}{3}+48\times 8+0.05$$

Subtract 768 from 128 to get -640.

$$-\frac{640}{3}+48\times 8+0.05$$

Multiply 48 and 8 to get 384.

$$-\frac{640}{3}+384+0.05$$

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

$$-\frac{640}{3}+\frac{1152}{3}+0.05$$

Since -\frac{640}{3} and \frac{1152}{3} have the same denominator, add them by adding their numerators.

$$\frac{-640+1152}{3}+0.05$$

Add -640 and 1152 to get 512.

$$\frac{512}{3}+0.05$$

Convert decimal number 0.05 to fraction \frac{5}{100}. Reduce the fraction \frac{5}{100} to lowest terms by extracting and canceling out 5.

$$\frac{512}{3}+\frac{1}{20}$$

Least common multiple of 3 and 20 is 60. Convert \frac{512}{3} and \frac{1}{20} to fractions with denominator 60.

$$\frac{10240}{60}+\frac{3}{60}$$

Since \frac{10240}{60} and \frac{3}{60} have the same denominator, add them by adding their numerators.

$$\frac{10240+3}{60}$$

Add 10240 and 3 to get 10243.

$$\frac{10243}{60}$$

Factor

$$\frac{10243}{3 \cdot 5 \cdot 2 ^ {2}} = 170\frac{43}{60} = 170.71666666666667$$