Solve ((frac{1/2)^{2}3^{-1}25^3}{(1/5)^-54^-29})^-1

$$( \frac { ( \frac { 1 } { 2 } ) ^ { 2 } 3 ^ { - 1 } 25 ^ { 3 } } { ( \frac { 1 } { 5 } ) ^ { - 5 } 4 ^ { - 2 } 9 } ) ^ { - 1 }$$

Evaluate

$$\frac{27}{20}=1.35$$

Solution Steps

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

$$\left(\frac{\frac{1}{4}\times 3^{-1}\times 25^{3}}{\left(\frac{1}{5}\right)^{-5}\times 4^{-2}\times 9}\right)^{-1}$$

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

$$\left(\frac{\frac{1}{4}\times \frac{1}{3}\times 25^{3}}{\left(\frac{1}{5}\right)^{-5}\times 4^{-2}\times 9}\right)^{-1}$$

Multiply \frac{1}{4} and \frac{1}{3} to get \frac{1}{12}.

$$\left(\frac{\frac{1}{12}\times 25^{3}}{\left(\frac{1}{5}\right)^{-5}\times 4^{-2}\times 9}\right)^{-1}$$

Calculate 25 to the power of 3 and get 15625.

$$\left(\frac{\frac{1}{12}\times 15625}{\left(\frac{1}{5}\right)^{-5}\times 4^{-2}\times 9}\right)^{-1}$$

Multiply \frac{1}{12} and 15625 to get \frac{15625}{12}.

$$\left(\frac{\frac{15625}{12}}{\left(\frac{1}{5}\right)^{-5}\times 4^{-2}\times 9}\right)^{-1}$$

Calculate \frac{1}{5} to the power of -5 and get 3125.

$$\left(\frac{\frac{15625}{12}}{3125\times 4^{-2}\times 9}\right)^{-1}$$

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

$$\left(\frac{\frac{15625}{12}}{3125\times \frac{1}{16}\times 9}\right)^{-1}$$

Multiply 3125 and \frac{1}{16} to get \frac{3125}{16}.

$$\left(\frac{\frac{15625}{12}}{\frac{3125}{16}\times 9}\right)^{-1}$$

Multiply \frac{3125}{16} and 9 to get \frac{28125}{16}.

$$\left(\frac{\frac{15625}{12}}{\frac{28125}{16}}\right)^{-1}$$

Divide \frac{15625}{12} by \frac{28125}{16} by multiplying \frac{15625}{12} by the reciprocal of \frac{28125}{16}.

$$\left(\frac{15625}{12}\times \frac{16}{28125}\right)^{-1}$$

Multiply \frac{15625}{12} and \frac{16}{28125} to get \frac{20}{27}.

$$\left(\frac{20}{27}\right)^{-1}$$

Calculate \frac{20}{27} to the power of -1 and get \frac{27}{20}.

$$\frac{27}{20}$$

Factor

$$\frac{3 ^ {3}}{2 ^ {2} \cdot 5} = 1\frac{7}{20} = 1.35$$