Solve frac{6^{-3}*4^-2-3}{2^3*5^-1*3^2}=

$$\frac { 6 ^ { - 3 } \cdot 4 ^ { - 2 } - 3 } { 2 ^ { 3 } \cdot 5 ^ { - 1 } \cdot 3 ^ { 2 } } =$$

Evaluate

$$-\frac{51835}{248832}\approx -0.208313239$$

Solution Steps

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

$$\frac{\frac{1}{216}\times 4^{-2}-3}{2^{3}\times 5^{-1}\times 3^{2}}$$

Calculate 4 to the power of -2 and get \frac{1}{16}.

$$\frac{\frac{1}{216}\times \frac{1}{16}-3}{2^{3}\times 5^{-1}\times 3^{2}}$$

Multiply \frac{1}{216} and \frac{1}{16} to get \frac{1}{3456}.

$$\frac{\frac{1}{3456}-3}{2^{3}\times 5^{-1}\times 3^{2}}$$

Subtract 3 from \frac{1}{3456} to get -\frac{10367}{3456}.

$$\frac{-\frac{10367}{3456}}{2^{3}\times 5^{-1}\times 3^{2}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{-\frac{10367}{3456}}{8\times 5^{-1}\times 3^{2}}$$

Calculate 5 to the power of -1 and get \frac{1}{5}.

$$\frac{-\frac{10367}{3456}}{8\times \frac{1}{5}\times 3^{2}}$$

Multiply 8 and \frac{1}{5} to get \frac{8}{5}.

$$\frac{-\frac{10367}{3456}}{\frac{8}{5}\times 3^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{-\frac{10367}{3456}}{\frac{8}{5}\times 9}$$

Multiply \frac{8}{5} and 9 to get \frac{72}{5}.

$$\frac{-\frac{10367}{3456}}{\frac{72}{5}}$$

Divide -\frac{10367}{3456} by \frac{72}{5} by multiplying -\frac{10367}{3456} by the reciprocal of \frac{72}{5}.

$$-\frac{10367}{3456}\times \frac{5}{72}$$

Multiply -\frac{10367}{3456} and \frac{5}{72} to get -\frac{51835}{248832}.

$$-\frac{51835}{248832}$$

Factor

$$-\frac{51835}{248832} = -0.2083132394547325$$