Solve [(7/8-2/5)*20/11-1/6]^2=[frac{5}{6}*(frac{1}{5}+frac{1}{10})]^3:(frac{2}{3}-frac{1}{4}*frac{5}{2})^2

$$[ ( \frac { 7 } { 8 } - \frac { 2 } { 5 } ) \cdot \frac { 20 } { 11 } - \frac { 1 } { 6 } ] ^ { 2 } = [ \frac { 5 } { 6 } \cdot ( \frac { 1 } { 5 } + \frac { 1 } { 10 } ) ] ^ { 3 } : ( \frac { 2 } { 3 } - \frac { 1 } { 4 } \cdot \frac { 5 } { 2 } ) ^ { 2 }$$

Verify

Solution Steps

Subtract \frac{2}{5} from \frac{7}{8} to get \frac{19}{40}.

$$\left(\frac{19}{40}\times \frac{20}{11}-\frac{1}{6}\right)^{2}=\frac{\left(\frac{5}{6}\left(\frac{1}{5}+\frac{1}{10}\right)\right)^{3}}{\left(\frac{2}{3}-\frac{1}{4}\times \frac{5}{2}\right)^{2}}$$

Multiply \frac{19}{40} and \frac{20}{11} to get \frac{19}{22}.

$$\left(\frac{19}{22}-\frac{1}{6}\right)^{2}=\frac{\left(\frac{5}{6}\left(\frac{1}{5}+\frac{1}{10}\right)\right)^{3}}{\left(\frac{2}{3}-\frac{1}{4}\times \frac{5}{2}\right)^{2}}$$

Subtract \frac{1}{6} from \frac{19}{22} to get \frac{23}{33}.

$$\left(\frac{23}{33}\right)^{2}=\frac{\left(\frac{5}{6}\left(\frac{1}{5}+\frac{1}{10}\right)\right)^{3}}{\left(\frac{2}{3}-\frac{1}{4}\times \frac{5}{2}\right)^{2}}$$

Calculate \frac{23}{33} to the power of 2 and get \frac{529}{1089}.

$$\frac{529}{1089}=\frac{\left(\frac{5}{6}\left(\frac{1}{5}+\frac{1}{10}\right)\right)^{3}}{\left(\frac{2}{3}-\frac{1}{4}\times \frac{5}{2}\right)^{2}}$$

Add \frac{1}{5} and \frac{1}{10} to get \frac{3}{10}.

$$\frac{529}{1089}=\frac{\left(\frac{5}{6}\times \frac{3}{10}\right)^{3}}{\left(\frac{2}{3}-\frac{1}{4}\times \frac{5}{2}\right)^{2}}$$

Multiply \frac{5}{6} and \frac{3}{10} to get \frac{1}{4}.

$$\frac{529}{1089}=\frac{\left(\frac{1}{4}\right)^{3}}{\left(\frac{2}{3}-\frac{1}{4}\times \frac{5}{2}\right)^{2}}$$

Calculate \frac{1}{4} to the power of 3 and get \frac{1}{64}.

$$\frac{529}{1089}=\frac{\frac{1}{64}}{\left(\frac{2}{3}-\frac{1}{4}\times \frac{5}{2}\right)^{2}}$$

Multiply \frac{1}{4} and \frac{5}{2} to get \frac{5}{8}.

$$\frac{529}{1089}=\frac{\frac{1}{64}}{\left(\frac{2}{3}-\frac{5}{8}\right)^{2}}$$

Subtract \frac{5}{8} from \frac{2}{3} to get \frac{1}{24}.

$$\frac{529}{1089}=\frac{\frac{1}{64}}{\left(\frac{1}{24}\right)^{2}}$$

Calculate \frac{1}{24} to the power of 2 and get \frac{1}{576}.

$$\frac{529}{1089}=\frac{\frac{1}{64}}{\frac{1}{576}}$$

Divide \frac{1}{64} by \frac{1}{576} by multiplying \frac{1}{64} by the reciprocal of \frac{1}{576}.

$$\frac{529}{1089}=\frac{1}{64}\times 576$$

Multiply \frac{1}{64} and 576 to get 9.

$$\frac{529}{1089}=9$$

Convert 9 to fraction \frac{9801}{1089}.

$$\frac{529}{1089}=\frac{9801}{1089}$$

Compare \frac{529}{1089} and \frac{9801}{1089}.

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