Solve [3/2:(6/20)^2-(2/3)^2*(4/9)^2]+frac{384}{23}

$$[ \frac { 3 } { 2 } : ( \frac { 6 } { 20 } ) ^ { 2 } - ( \frac { 2 } { 3 } ) ^ { 2 } \cdot ( \frac { 4 } { 9 } ) ^ { 2 } ] + \frac { 384 } { 23 }$$

Evaluate

$$\frac{557914}{16767}\approx 33.274527345$$

Solution Steps

Reduce the fraction \frac{6}{20} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{3}{2}}{\left(\frac{3}{10}\right)^{2}}-\left(\frac{2}{3}\right)^{2}\times \left(\frac{4}{9}\right)^{2}+\frac{384}{23}$$

Calculate \frac{3}{10} to the power of 2 and get \frac{9}{100}.

$$\frac{\frac{3}{2}}{\frac{9}{100}}-\left(\frac{2}{3}\right)^{2}\times \left(\frac{4}{9}\right)^{2}+\frac{384}{23}$$

Divide \frac{3}{2} by \frac{9}{100} by multiplying \frac{3}{2} by the reciprocal of \frac{9}{100}.

$$\frac{3}{2}\times \frac{100}{9}-\left(\frac{2}{3}\right)^{2}\times \left(\frac{4}{9}\right)^{2}+\frac{384}{23}$$

Multiply \frac{3}{2} and \frac{100}{9} to get \frac{50}{3}.

$$\frac{50}{3}-\left(\frac{2}{3}\right)^{2}\times \left(\frac{4}{9}\right)^{2}+\frac{384}{23}$$

Calculate \frac{2}{3} to the power of 2 and get \frac{4}{9}.

$$\frac{50}{3}-\frac{4}{9}\times \left(\frac{4}{9}\right)^{2}+\frac{384}{23}$$

Calculate \frac{4}{9} to the power of 2 and get \frac{16}{81}.

$$\frac{50}{3}-\frac{4}{9}\times \frac{16}{81}+\frac{384}{23}$$

Multiply \frac{4}{9} and \frac{16}{81} to get \frac{64}{729}.

$$\frac{50}{3}-\frac{64}{729}+\frac{384}{23}$$

Subtract \frac{64}{729} from \frac{50}{3} to get \frac{12086}{729}.

$$\frac{12086}{729}+\frac{384}{23}$$

Add \frac{12086}{729} and \frac{384}{23} to get \frac{557914}{16767}.

$$\frac{557914}{16767}$$

Factor

$$\frac{2 \cdot 7 ^ {2} \cdot 5693}{3 ^ {6} \cdot 23} = 33\frac{4603}{16767} = 33.27452734538081$$