Solve [(1/2)^3-(1/6)^3]:128-20^1/65:5

$$[ ( \frac { 1 } { 2 } ) ^ { 3 } - ( \frac { 1 } { 6 } ) ^ { 3 } ] : \frac { 128 - 20 ^ { 1 } } { 65 : 5 }$$

Evaluate

$$\frac{169}{11664}\approx 0.014489026$$

Solution Steps

Calculate \frac{1}{2} to the power of 3 and get \frac{1}{8}.

$$\frac{\frac{1}{8}-\left(\frac{1}{6}\right)^{3}}{\frac{128-20^{1}}{\frac{65}{5}}}$$

Calculate \frac{1}{6} to the power of 3 and get \frac{1}{216}.

$$\frac{\frac{1}{8}-\frac{1}{216}}{\frac{128-20^{1}}{\frac{65}{5}}}$$

Least common multiple of 8 and 216 is 216. Convert \frac{1}{8} and \frac{1}{216} to fractions with denominator 216.

$$\frac{\frac{27}{216}-\frac{1}{216}}{\frac{128-20^{1}}{\frac{65}{5}}}$$

Since \frac{27}{216} and \frac{1}{216} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{27-1}{216}}{\frac{128-20^{1}}{\frac{65}{5}}}$$

Subtract 1 from 27 to get 26.

$$\frac{\frac{26}{216}}{\frac{128-20^{1}}{\frac{65}{5}}}$$

Reduce the fraction \frac{26}{216} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{13}{108}}{\frac{128-20^{1}}{\frac{65}{5}}}$$

Calculate 20 to the power of 1 and get 20.

$$\frac{\frac{13}{108}}{\frac{128-20}{\frac{65}{5}}}$$

Subtract 20 from 128 to get 108.

$$\frac{\frac{13}{108}}{\frac{108}{\frac{65}{5}}}$$

Divide 65 by 5 to get 13.

$$\frac{\frac{13}{108}}{\frac{108}{13}}$$

Divide \frac{13}{108} by \frac{108}{13} by multiplying \frac{13}{108} by the reciprocal of \frac{108}{13}.

$$\frac{13}{108}\times \frac{13}{108}$$

Multiply \frac{13}{108} times \frac{13}{108} by multiplying numerator times numerator and denominator times denominator.

$$\frac{13\times 13}{108\times 108}$$

Do the multiplications in the fraction \frac{13\times 13}{108\times 108}.

$$\frac{169}{11664}$$

Factor

$$\frac{13 ^ {2}}{2 ^ {4} \cdot 3 ^ {6}} = 0.014489026063100137$$