Solve (0,3+1/2)^2*[(1/3)^-2-(14/5)^2]^-1

$$( 0,3 + \frac { 1 } { 2 } ) ^ { 2 } \cdot [ ( \frac { 1 } { 3 } ) ^ { - 2 } - ( \frac { 14 } { 5 } ) ^ { 2 } ] ^ { - 1 }$$

Evaluate

$$\frac{16}{29}\approx 0,551724138$$

Solution Steps

Add 0,3 and \frac{1}{2} to get \frac{4}{5}.

$$\left(\frac{4}{5}\right)^{2}\left(\left(\frac{1}{3}\right)^{-2}-\left(\frac{14}{5}\right)^{2}\right)^{-1}$$

Calculate \frac{4}{5} to the power of 2 and get \frac{16}{25}.

$$\frac{16}{25}\left(\left(\frac{1}{3}\right)^{-2}-\left(\frac{14}{5}\right)^{2}\right)^{-1}$$

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

$$\frac{16}{25}\left(9-\left(\frac{14}{5}\right)^{2}\right)^{-1}$$

Calculate \frac{14}{5} to the power of 2 and get \frac{196}{25}.

$$\frac{16}{25}\left(9-\frac{196}{25}\right)^{-1}$$

Subtract \frac{196}{25} from 9 to get \frac{29}{25}.

$$\frac{16}{25}\times \left(\frac{29}{25}\right)^{-1}$$

Calculate \frac{29}{25} to the power of -1 and get \frac{25}{29}.

$$\frac{16}{25}\times \frac{25}{29}$$

Multiply \frac{16}{25} and \frac{25}{29} to get \frac{16}{29}.

$$\frac{16}{29}$$

Factor

$$\frac{2 ^ {4}}{29} = 0.5517241379310345$$