Solve (frac{(sqrt{27})^{2}*125^-1}{9^-3*25^-1})^-3

$$( \frac { ( \sqrt { 27 } ) ^ { 2 } \cdot 125 ^ { - 1 } } { 9 ^ { - 3 } \cdot 25 ^ { - 1 } } ) ^ { - 3 }$$

Evaluate

$$\frac{125}{7625597484987}\approx 1.639215815 \cdot 10^{-11}$$

Solution Steps

The square of \sqrt{27} is 27.

$$\left(\frac{27\times 125^{-1}}{9^{-3}\times 25^{-1}}\right)^{-3}$$

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

$$\left(\frac{27\times \frac{1}{125}}{9^{-3}\times 25^{-1}}\right)^{-3}$$

Multiply 27 and \frac{1}{125} to get \frac{27}{125}.

$$\left(\frac{\frac{27}{125}}{9^{-3}\times 25^{-1}}\right)^{-3}$$

Calculate 9 to the power of -3 and get \frac{1}{729}.

$$\left(\frac{\frac{27}{125}}{\frac{1}{729}\times 25^{-1}}\right)^{-3}$$

Calculate 25 to the power of -1 and get \frac{1}{25}.

$$\left(\frac{\frac{27}{125}}{\frac{1}{729}\times \frac{1}{25}}\right)^{-3}$$

Multiply \frac{1}{729} and \frac{1}{25} to get \frac{1}{18225}.

$$\left(\frac{\frac{27}{125}}{\frac{1}{18225}}\right)^{-3}$$

Divide \frac{27}{125} by \frac{1}{18225} by multiplying \frac{27}{125} by the reciprocal of \frac{1}{18225}.

$$\left(\frac{27}{125}\times 18225\right)^{-3}$$

Multiply \frac{27}{125} and 18225 to get \frac{19683}{5}.

$$\left(\frac{19683}{5}\right)^{-3}$$

Calculate \frac{19683}{5} to the power of -3 and get \frac{125}{7625597484987}.

$$\frac{125}{7625597484987}$$

Factor

$$\frac{5 ^ {3}}{3 ^ {27}} = 1.6392158154963659 \times 10^{-11}$$