Solve frac{5^{-3}+81(3/5)^-4(-1/5)^6}{(1/12)^0-15*5^-3}

$$\frac { 5 ^ { - 3 } + 81 ( \frac { 3 } { 5 } ) ^ { - 4 } ( - \frac { 1 } { 5 } ) ^ { 6 } } { ( \frac { 1 } { 12 } ) ^ { 0 } - 15 \cdot 5 ^ { - 3 } }$$

Evaluate

$$\frac{3}{55}\approx 0.054545455$$

Solution Steps

Calculate 5 to the power of -3 and get \frac{1}{125}.

$$\frac{\frac{1}{125}+81\times \left(\frac{3}{5}\right)^{-4}\left(-\frac{1}{5}\right)^{6}}{\left(\frac{1}{12}\right)^{0}-15\times 5^{-3}}$$

Calculate \frac{3}{5} to the power of -4 and get \frac{625}{81}.

$$\frac{\frac{1}{125}+81\times \frac{625}{81}\left(-\frac{1}{5}\right)^{6}}{\left(\frac{1}{12}\right)^{0}-15\times 5^{-3}}$$

Multiply 81 and \frac{625}{81} to get 625.

$$\frac{\frac{1}{125}+625\left(-\frac{1}{5}\right)^{6}}{\left(\frac{1}{12}\right)^{0}-15\times 5^{-3}}$$

Calculate -\frac{1}{5} to the power of 6 and get \frac{1}{15625}.

$$\frac{\frac{1}{125}+625\times \frac{1}{15625}}{\left(\frac{1}{12}\right)^{0}-15\times 5^{-3}}$$

Multiply 625 and \frac{1}{15625} to get \frac{1}{25}.

$$\frac{\frac{1}{125}+\frac{1}{25}}{\left(\frac{1}{12}\right)^{0}-15\times 5^{-3}}$$

Add \frac{1}{125} and \frac{1}{25} to get \frac{6}{125}.

$$\frac{\frac{6}{125}}{\left(\frac{1}{12}\right)^{0}-15\times 5^{-3}}$$

Calculate \frac{1}{12} to the power of 0 and get 1.

$$\frac{\frac{6}{125}}{1-15\times 5^{-3}}$$

Calculate 5 to the power of -3 and get \frac{1}{125}.

$$\frac{\frac{6}{125}}{1-15\times \frac{1}{125}}$$

Multiply 15 and \frac{1}{125} to get \frac{3}{25}.

$$\frac{\frac{6}{125}}{1-\frac{3}{25}}$$

Subtract \frac{3}{25} from 1 to get \frac{22}{25}.

$$\frac{\frac{6}{125}}{\frac{22}{25}}$$

Divide \frac{6}{125} by \frac{22}{25} by multiplying \frac{6}{125} by the reciprocal of \frac{22}{25}.

$$\frac{6}{125}\times \frac{25}{22}$$

Multiply \frac{6}{125} and \frac{25}{22} to get \frac{3}{55}.

$$\frac{3}{55}$$

Factor

$$\frac{3}{5 \cdot 11} = 0.05454545454545454$$