Solve {left(52.16^2/6+frac{12.012^2/5right)}^2}{12.812^4/5*4+52.16^4/6*5}

$$\frac{ { \left( \frac{ { 52.16 }^{ 2 } }{ 6 } + \frac{ { 12.012 }^{ 2 } }{ 5 } \right) }^{ 2 } }{ \frac{ { 12.812 }^{ 4 } }{ 5 \cdot 4 } + \frac{ { 52.16 }^{ 4 } }{ 6 \cdot 5 } }$$

Evaluate

$$\frac{817787525522130916}{872160683535555645}\approx 0.937656949$$

Solution Steps

Calculate 52.16 to the power of 2 and get 2720.6656.

$$\frac{\left(\frac{2720.6656}{6}+\frac{12.012^{2}}{5}\right)^{2}}{\frac{12.812^{4}}{5\times 4}+\frac{52.16^{4}}{6\times 5}}$$

Expand \frac{2720.6656}{6} by multiplying both numerator and the denominator by 10000.

$$\frac{\left(\frac{27206656}{60000}+\frac{12.012^{2}}{5}\right)^{2}}{\frac{12.812^{4}}{5\times 4}+\frac{52.16^{4}}{6\times 5}}$$

Reduce the fraction \frac{27206656}{60000} to lowest terms by extracting and canceling out 32.

$$\frac{\left(\frac{850208}{1875}+\frac{12.012^{2}}{5}\right)^{2}}{\frac{12.812^{4}}{5\times 4}+\frac{52.16^{4}}{6\times 5}}$$

Calculate 12.012 to the power of 2 and get 144.288144.

$$\frac{\left(\frac{850208}{1875}+\frac{144.288144}{5}\right)^{2}}{\frac{12.812^{4}}{5\times 4}+\frac{52.16^{4}}{6\times 5}}$$

Expand \frac{144.288144}{5} by multiplying both numerator and the denominator by 1000000.

$$\frac{\left(\frac{850208}{1875}+\frac{144288144}{5000000}\right)^{2}}{\frac{12.812^{4}}{5\times 4}+\frac{52.16^{4}}{6\times 5}}$$

Reduce the fraction \frac{144288144}{5000000} to lowest terms by extracting and canceling out 16.

$$\frac{\left(\frac{850208}{1875}+\frac{9018009}{312500}\right)^{2}}{\frac{12.812^{4}}{5\times 4}+\frac{52.16^{4}}{6\times 5}}$$

Add \frac{850208}{1875} and \frac{9018009}{312500} to get \frac{452158027}{937500}.

$$\frac{\left(\frac{452158027}{937500}\right)^{2}}{\frac{12.812^{4}}{5\times 4}+\frac{52.16^{4}}{6\times 5}}$$

Calculate \frac{452158027}{937500} to the power of 2 and get \frac{204446881380532729}{878906250000}.

$$\frac{\frac{204446881380532729}{878906250000}}{\frac{12.812^{4}}{5\times 4}+\frac{52.16^{4}}{6\times 5}}$$

Calculate 12.812 to the power of 4 and get 26944.350542254336.

$$\frac{\frac{204446881380532729}{878906250000}}{\frac{26944.350542254336}{5\times 4}+\frac{52.16^{4}}{6\times 5}}$$

Multiply 5 and 4 to get 20.

$$\frac{\frac{204446881380532729}{878906250000}}{\frac{26944.350542254336}{20}+\frac{52.16^{4}}{6\times 5}}$$

Expand \frac{26944.350542254336}{20} by multiplying both numerator and the denominator by 1000000000000.

$$\frac{\frac{204446881380532729}{878906250000}}{\frac{26944350542254336}{20000000000000}+\frac{52.16^{4}}{6\times 5}}$$

Reduce the fraction \frac{26944350542254336}{20000000000000} to lowest terms by extracting and canceling out 256.

$$\frac{\frac{204446881380532729}{878906250000}}{\frac{105251369305681}{78125000000}+\frac{52.16^{4}}{6\times 5}}$$

Calculate 52.16 to the power of 4 and get 7402021.30702336.

$$\frac{\frac{204446881380532729}{878906250000}}{\frac{105251369305681}{78125000000}+\frac{7402021.30702336}{6\times 5}}$$

Multiply 6 and 5 to get 30.

$$\frac{\frac{204446881380532729}{878906250000}}{\frac{105251369305681}{78125000000}+\frac{7402021.30702336}{30}}$$

Expand \frac{7402021.30702336}{30} by multiplying both numerator and the denominator by 100000000.

$$\frac{\frac{204446881380532729}{878906250000}}{\frac{105251369305681}{78125000000}+\frac{740202130702336}{3000000000}}$$

Reduce the fraction \frac{740202130702336}{3000000000} to lowest terms by extracting and canceling out 512.

$$\frac{\frac{204446881380532729}{878906250000}}{\frac{105251369305681}{78125000000}+\frac{1445707286528}{5859375}}$$

Add \frac{105251369305681}{78125000000} and \frac{1445707286528}{5859375} to get \frac{58144045569037043}{234375000000}.

$$\frac{\frac{204446881380532729}{878906250000}}{\frac{58144045569037043}{234375000000}}$$

Divide \frac{204446881380532729}{878906250000} by \frac{58144045569037043}{234375000000} by multiplying \frac{204446881380532729}{878906250000} by the reciprocal of \frac{58144045569037043}{234375000000}.

$$\frac{204446881380532729}{878906250000}\times \frac{234375000000}{58144045569037043}$$

Multiply \frac{204446881380532729}{878906250000} and \frac{234375000000}{58144045569037043} to get \frac{817787525522130916}{872160683535555645}.

$$\frac{817787525522130916}{872160683535555645}$$

Factor

$$\frac{2 ^ {2} \cdot 17 ^ {2} \cdot 26597531 ^ {2}}{3 \cdot 5 \cdot 11 \cdot 241 \cdot 447609647257 \cdot 7 ^ {2}} = 0.9376569489546269$$