Solve {left(4345^2/11+frac{33622^2/18right)}^2}{4375^4/11left(11-1right)+3362^4/18left(18-1right)}=19

$$\frac{ { \left( \frac{ 43 { 45 }^{ 2 } }{ 11 } + \frac{ 33 { 622 }^{ 2 } }{ 18 } \right) }^{ 2 } }{ \frac{ 43 { 75 }^{ 4 } }{ 11 \left( 11-1 \right) } + \frac{ 33 { 62 }^{ 4 } }{ 18 \left( 18-1 \right) } } = 19$$

Verify

Solution Steps

Calculate 45 to the power of 2 and get 2025.

$$\frac{\left(\frac{43\times 2025}{11}+\frac{33\times 622^{2}}{18}\right)^{2}}{\frac{43\times 75^{4}}{11\left(11-1\right)}+\frac{33\times 62^{4}}{18\left(18-1\right)}}=19$$

Multiply 43 and 2025 to get 87075.

$$\frac{\left(\frac{87075}{11}+\frac{33\times 622^{2}}{18}\right)^{2}}{\frac{43\times 75^{4}}{11\left(11-1\right)}+\frac{33\times 62^{4}}{18\left(18-1\right)}}=19$$

Calculate 622 to the power of 2 and get 386884.

$$\frac{\left(\frac{87075}{11}+\frac{33\times 386884}{18}\right)^{2}}{\frac{43\times 75^{4}}{11\left(11-1\right)}+\frac{33\times 62^{4}}{18\left(18-1\right)}}=19$$

Multiply 33 and 386884 to get 12767172.

$$\frac{\left(\frac{87075}{11}+\frac{12767172}{18}\right)^{2}}{\frac{43\times 75^{4}}{11\left(11-1\right)}+\frac{33\times 62^{4}}{18\left(18-1\right)}}=19$$

Reduce the fraction \frac{12767172}{18} to lowest terms by extracting and canceling out 6.

$$\frac{\left(\frac{87075}{11}+\frac{2127862}{3}\right)^{2}}{\frac{43\times 75^{4}}{11\left(11-1\right)}+\frac{33\times 62^{4}}{18\left(18-1\right)}}=19$$

Add \frac{87075}{11} and \frac{2127862}{3} to get \frac{23667707}{33}.

$$\frac{\left(\frac{23667707}{33}\right)^{2}}{\frac{43\times 75^{4}}{11\left(11-1\right)}+\frac{33\times 62^{4}}{18\left(18-1\right)}}=19$$

Calculate \frac{23667707}{33} to the power of 2 and get \frac{560160354637849}{1089}.

$$\frac{\frac{560160354637849}{1089}}{\frac{43\times 75^{4}}{11\left(11-1\right)}+\frac{33\times 62^{4}}{18\left(18-1\right)}}=19$$

Calculate 75 to the power of 4 and get 31640625.

$$\frac{\frac{560160354637849}{1089}}{\frac{43\times 31640625}{11\left(11-1\right)}+\frac{33\times 62^{4}}{18\left(18-1\right)}}=19$$

Multiply 43 and 31640625 to get 1360546875.

$$\frac{\frac{560160354637849}{1089}}{\frac{1360546875}{11\left(11-1\right)}+\frac{33\times 62^{4}}{18\left(18-1\right)}}=19$$

Subtract 1 from 11 to get 10.

$$\frac{\frac{560160354637849}{1089}}{\frac{1360546875}{11\times 10}+\frac{33\times 62^{4}}{18\left(18-1\right)}}=19$$

Multiply 11 and 10 to get 110.

$$\frac{\frac{560160354637849}{1089}}{\frac{1360546875}{110}+\frac{33\times 62^{4}}{18\left(18-1\right)}}=19$$

Reduce the fraction \frac{1360546875}{110} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{560160354637849}{1089}}{\frac{272109375}{22}+\frac{33\times 62^{4}}{18\left(18-1\right)}}=19$$

Cancel out 3 in both numerator and denominator.

$$\frac{\frac{560160354637849}{1089}}{\frac{272109375}{22}+\frac{11\times 62^{4}}{6\left(18-1\right)}}=19$$

Calculate 62 to the power of 4 and get 14776336.

$$\frac{\frac{560160354637849}{1089}}{\frac{272109375}{22}+\frac{11\times 14776336}{6\left(18-1\right)}}=19$$

Multiply 11 and 14776336 to get 162539696.

$$\frac{\frac{560160354637849}{1089}}{\frac{272109375}{22}+\frac{162539696}{6\left(18-1\right)}}=19$$

Subtract 1 from 18 to get 17.

$$\frac{\frac{560160354637849}{1089}}{\frac{272109375}{22}+\frac{162539696}{6\times 17}}=19$$

Multiply 6 and 17 to get 102.

$$\frac{\frac{560160354637849}{1089}}{\frac{272109375}{22}+\frac{162539696}{102}}=19$$

Reduce the fraction \frac{162539696}{102} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{560160354637849}{1089}}{\frac{272109375}{22}+\frac{81269848}{51}}=19$$

Add \frac{272109375}{22} and \frac{81269848}{51} to get \frac{15665514781}{1122}.

$$\frac{\frac{560160354637849}{1089}}{\frac{15665514781}{1122}}=19$$

Divide \frac{560160354637849}{1089} by \frac{15665514781}{1122} by multiplying \frac{560160354637849}{1089} by the reciprocal of \frac{15665514781}{1122}.

$$\frac{560160354637849}{1089}\times \frac{1122}{15665514781}=19$$

Multiply \frac{560160354637849}{1089} and \frac{1122}{15665514781} to get \frac{2720778865383838}{73851712539}.

$$\frac{2720778865383838}{73851712539}=19$$

Convert 19 to fraction \frac{1403182538241}{73851712539}.

$$\frac{2720778865383838}{73851712539}=\frac{1403182538241}{73851712539}$$

Compare \frac{2720778865383838}{73851712539} and \frac{1403182538241}{73851712539}.

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