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

$$( 2 ^ { 5 } \cdot 3 ^ { - 2 } \cdot 1 T ^ { - 1 } ) ^ { - 2 }$$

Evaluate

$$\frac{81T^{2}}{1024}$$

Solution Steps

Calculate 2 to the power of 5 and get 32.

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

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

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

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

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

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

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

Expand \left(\frac{32}{9}T^{-1}\right)^{-2}.

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

To raise a power to another power, multiply the exponents. Multiply -1 and -2 to get 2.

$$\left(\frac{32}{9}\right)^{-2}T^{2}$$

Calculate \frac{32}{9} to the power of -2 and get \frac{81}{1024}.

$$\frac{81}{1024}T^{2}$$

Expand

$$\frac{81T^{2}}{1024}$$

Solution Steps

Calculate 2 to the power of 5 and get 32.

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

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

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

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

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

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

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

Expand \left(\frac{32}{9}T^{-1}\right)^{-2}.

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

To raise a power to another power, multiply the exponents. Multiply -1 and -2 to get 2.

$$\left(\frac{32}{9}\right)^{-2}T^{2}$$

Calculate \frac{32}{9} to the power of -2 and get \frac{81}{1024}.

$$\frac{81}{1024}T^{2}$$