Solve frac{(frac{5.160^{2}}{6}+12.012^2/5)^2}{12.812^4/5*4+52.160^4/6*5}

$$\frac { ( \frac { 5.160 ^ { 2 } } { 6 } + \frac { 12.012 ^ { 2 } } { 5 } ) ^ { 2 } } { \frac { 12.812 ^ { 4 } } { 5 \times 4 } + \frac { 52.160 ^ { 4 } } { 6 \times 5 } }$$

Evaluate

$$\frac{1299108118176972}{290720227845185215}\approx 0.004468585$$

Solution Steps

Calculate 5.16 to the power of 2 and get 26.6256.

$$\frac{\left(\frac{26.6256}{6}+\frac{12.012^{2}}{5}\right)^{2}}{\frac{12.812^{4}}{5\times 4}+\frac{52.16^{4}}{6\times 5}}$$

Expand \frac{26.6256}{6} by multiplying both numerator and the denominator by 10000.

$$\frac{\left(\frac{266256}{60000}+\frac{12.012^{2}}{5}\right)^{2}}{\frac{12.812^{4}}{5\times 4}+\frac{52.16^{4}}{6\times 5}}$$

Reduce the fraction \frac{266256}{60000} to lowest terms by extracting and canceling out 48.

$$\frac{\left(\frac{5547}{1250}+\frac{12.012^{2}}{5}\right)^{2}}{\frac{12.812^{4}}{5\times 4}+\frac{52.16^{4}}{6\times 5}}$$

Calculate 12.012 to the power of 2 and get 144.288144.

$$\frac{\left(\frac{5547}{1250}+\frac{144.288144}{5}\right)^{2}}{\frac{12.812^{4}}{5\times 4}+\frac{52.16^{4}}{6\times 5}}$$

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

$$\frac{\left(\frac{5547}{1250}+\frac{144288144}{5000000}\right)^{2}}{\frac{12.812^{4}}{5\times 4}+\frac{52.16^{4}}{6\times 5}}$$

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

$$\frac{\left(\frac{5547}{1250}+\frac{9018009}{312500}\right)^{2}}{\frac{12.812^{4}}{5\times 4}+\frac{52.16^{4}}{6\times 5}}$$

Add \frac{5547}{1250} and \frac{9018009}{312500} to get \frac{10404759}{312500}.

$$\frac{\left(\frac{10404759}{312500}\right)^{2}}{\frac{12.812^{4}}{5\times 4}+\frac{52.16^{4}}{6\times 5}}$$

Calculate \frac{10404759}{312500} to the power of 2 and get \frac{108259009848081}{97656250000}.

$$\frac{\frac{108259009848081}{97656250000}}{\frac{12.812^{4}}{5\times 4}+\frac{52.16^{4}}{6\times 5}}$$

Calculate 12.812 to the power of 4 and get 26944.350542254336.

$$\frac{\frac{108259009848081}{97656250000}}{\frac{26944.350542254336}{5\times 4}+\frac{52.16^{4}}{6\times 5}}$$

Multiply 5 and 4 to get 20.

$$\frac{\frac{108259009848081}{97656250000}}{\frac{26944.350542254336}{20}+\frac{52.16^{4}}{6\times 5}}$$

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

$$\frac{\frac{108259009848081}{97656250000}}{\frac{26944350542254336}{20000000000000}+\frac{52.16^{4}}{6\times 5}}$$

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

$$\frac{\frac{108259009848081}{97656250000}}{\frac{105251369305681}{78125000000}+\frac{52.16^{4}}{6\times 5}}$$

Calculate 52.16 to the power of 4 and get 7402021.30702336.

$$\frac{\frac{108259009848081}{97656250000}}{\frac{105251369305681}{78125000000}+\frac{7402021.30702336}{6\times 5}}$$

Multiply 6 and 5 to get 30.

$$\frac{\frac{108259009848081}{97656250000}}{\frac{105251369305681}{78125000000}+\frac{7402021.30702336}{30}}$$

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

$$\frac{\frac{108259009848081}{97656250000}}{\frac{105251369305681}{78125000000}+\frac{740202130702336}{3000000000}}$$

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

$$\frac{\frac{108259009848081}{97656250000}}{\frac{105251369305681}{78125000000}+\frac{1445707286528}{5859375}}$$

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

$$\frac{\frac{108259009848081}{97656250000}}{\frac{58144045569037043}{234375000000}}$$

Divide \frac{108259009848081}{97656250000} by \frac{58144045569037043}{234375000000} by multiplying \frac{108259009848081}{97656250000} by the reciprocal of \frac{58144045569037043}{234375000000}.

$$\frac{108259009848081}{97656250000}\times \frac{234375000000}{58144045569037043}$$

Multiply \frac{108259009848081}{97656250000} and \frac{234375000000}{58144045569037043} to get \frac{1299108118176972}{290720227845185215}.

$$\frac{1299108118176972}{290720227845185215}$$

Factor

$$\frac{2 ^ {2} \cdot 3 ^ {3} \cdot 3468253 ^ {2}}{5 \cdot 11 \cdot 241 \cdot 447609647257 \cdot 7 ^ {2}} = 0.00446858523676163$$