Solve {[(2-frac{6^{2}}{5^{2}})*15-2^3]^2*[(2+3/2+2/3:2/15):1/10-10]-3^2}^2:frac{9}{2}

$$\{ [ ( 2 - \frac { 6 ^ { 2 } } { 5 ^ { 2 } } ) \cdot 15 - 2 ^ { 3 } ] ^ { 2 } \cdot [ ( 2 + \frac { 3 } { 2 } + \frac { 2 } { 3 } : \frac { 2 } { 15 } ) : \frac { 1 } { 10 } - 10 ] - 3 ^ { 2 } \} ^ { 2 } : \frac { 9 } { 2 }$$

Evaluate

$$2$$

Solution Steps

Calculate 6 to the power of 2 and get 36.

$$\frac{\left(\left(\left(2-\frac{36}{5^{2}}\right)\times 15-2^{3}\right)^{2}\left(\frac{2+\frac{3}{2}+\frac{\frac{2}{3}}{\frac{2}{15}}}{\frac{1}{10}}-10\right)-3^{2}\right)^{2}}{\frac{9}{2}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{\left(\left(\left(2-\frac{36}{25}\right)\times 15-2^{3}\right)^{2}\left(\frac{2+\frac{3}{2}+\frac{\frac{2}{3}}{\frac{2}{15}}}{\frac{1}{10}}-10\right)-3^{2}\right)^{2}}{\frac{9}{2}}$$

Subtract \frac{36}{25} from 2 to get \frac{14}{25}.

$$\frac{\left(\left(\frac{14}{25}\times 15-2^{3}\right)^{2}\left(\frac{2+\frac{3}{2}+\frac{\frac{2}{3}}{\frac{2}{15}}}{\frac{1}{10}}-10\right)-3^{2}\right)^{2}}{\frac{9}{2}}$$

Multiply \frac{14}{25} and 15 to get \frac{42}{5}.

$$\frac{\left(\left(\frac{42}{5}-2^{3}\right)^{2}\left(\frac{2+\frac{3}{2}+\frac{\frac{2}{3}}{\frac{2}{15}}}{\frac{1}{10}}-10\right)-3^{2}\right)^{2}}{\frac{9}{2}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{\left(\left(\frac{42}{5}-8\right)^{2}\left(\frac{2+\frac{3}{2}+\frac{\frac{2}{3}}{\frac{2}{15}}}{\frac{1}{10}}-10\right)-3^{2}\right)^{2}}{\frac{9}{2}}$$

Subtract 8 from \frac{42}{5} to get \frac{2}{5}.

$$\frac{\left(\left(\frac{2}{5}\right)^{2}\left(\frac{2+\frac{3}{2}+\frac{\frac{2}{3}}{\frac{2}{15}}}{\frac{1}{10}}-10\right)-3^{2}\right)^{2}}{\frac{9}{2}}$$

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

$$\frac{\left(\frac{4}{25}\left(\frac{2+\frac{3}{2}+\frac{\frac{2}{3}}{\frac{2}{15}}}{\frac{1}{10}}-10\right)-3^{2}\right)^{2}}{\frac{9}{2}}$$

Add 2 and \frac{3}{2} to get \frac{7}{2}.

$$\frac{\left(\frac{4}{25}\left(\frac{\frac{7}{2}+\frac{\frac{2}{3}}{\frac{2}{15}}}{\frac{1}{10}}-10\right)-3^{2}\right)^{2}}{\frac{9}{2}}$$

Divide \frac{2}{3} by \frac{2}{15} by multiplying \frac{2}{3} by the reciprocal of \frac{2}{15}.

$$\frac{\left(\frac{4}{25}\left(\frac{\frac{7}{2}+\frac{2}{3}\times \frac{15}{2}}{\frac{1}{10}}-10\right)-3^{2}\right)^{2}}{\frac{9}{2}}$$

Multiply \frac{2}{3} and \frac{15}{2} to get 5.

$$\frac{\left(\frac{4}{25}\left(\frac{\frac{7}{2}+5}{\frac{1}{10}}-10\right)-3^{2}\right)^{2}}{\frac{9}{2}}$$

Add \frac{7}{2} and 5 to get \frac{17}{2}.

$$\frac{\left(\frac{4}{25}\left(\frac{\frac{17}{2}}{\frac{1}{10}}-10\right)-3^{2}\right)^{2}}{\frac{9}{2}}$$

Divide \frac{17}{2} by \frac{1}{10} by multiplying \frac{17}{2} by the reciprocal of \frac{1}{10}.

$$\frac{\left(\frac{4}{25}\left(\frac{17}{2}\times 10-10\right)-3^{2}\right)^{2}}{\frac{9}{2}}$$

Multiply \frac{17}{2} and 10 to get 85.

$$\frac{\left(\frac{4}{25}\left(85-10\right)-3^{2}\right)^{2}}{\frac{9}{2}}$$

Subtract 10 from 85 to get 75.

$$\frac{\left(\frac{4}{25}\times 75-3^{2}\right)^{2}}{\frac{9}{2}}$$

Multiply \frac{4}{25} and 75 to get 12.

$$\frac{\left(12-3^{2}\right)^{2}}{\frac{9}{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{\left(12-9\right)^{2}}{\frac{9}{2}}$$

Subtract 9 from 12 to get 3.

$$\frac{3^{2}}{\frac{9}{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{9}{\frac{9}{2}}$$

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

$$9\times \frac{2}{9}$$

Multiply 9 and \frac{2}{9} to get 2.

$$2$$

Factor

$$2$$