Solve (2^5*3^-2*11^-1)^-2

$$( 2 ^ { 5 } \times 3 ^ { - 2 } \times 11 ^ { - 1 } ) ^ { - 2 }$$

Evaluate

$$\frac{9801}{1024}=9.571289062$$

Solution Steps

Calculate 2 to the power of 5 and get 32.

$$\left(32\times 3^{-2}\times 11^{-1}\right)^{-2}$$

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$\left(32\times \frac{1}{9}\times 11^{-1}\right)^{-2}$$

Multiply 32 and \frac{1}{9} to get \frac{32}{9}.

$$\left(\frac{32}{9}\times 11^{-1}\right)^{-2}$$

Calculate 11 to the power of -1 and get \frac{1}{11}.

$$\left(\frac{32}{9}\times \frac{1}{11}\right)^{-2}$$

Multiply \frac{32}{9} and \frac{1}{11} to get \frac{32}{99}.

$$\left(\frac{32}{99}\right)^{-2}$$

Calculate \frac{32}{99} to the power of -2 and get \frac{9801}{1024}.

$$\frac{9801}{1024}$$

Factor

$$\frac{3 ^ {4} \cdot 11 ^ {2}}{2 ^ {10}} = 9\frac{585}{1024} = 9.5712890625$$