Solve 300*left(37*143-35*85right)^22/72*228*178*122=

$$\frac{ 300 \times { \left(37 \times 143-35 \times 85 \right) }^{ 22 } }{ 72 \times 228 \times 178 \times 122 } =$$

Evaluate

$$\frac{9179007656826681663906316878299626440326086423744031827229204191956172800}{103151}\approx 8.898612381 \cdot 10^{67}$$

Solution Steps

Cancel out 12 in both numerator and denominator.

$$\frac{25\left(37\times 143-35\times 85\right)^{22}}{6\times 122\times 178\times 228}$$

Multiply 37 and 143 to get 5291.

$$\frac{25\left(5291-35\times 85\right)^{22}}{6\times 122\times 178\times 228}$$

Multiply 35 and 85 to get 2975.

$$\frac{25\left(5291-2975\right)^{22}}{6\times 122\times 178\times 228}$$

Subtract 2975 from 5291 to get 2316.

$$\frac{25\times 2316^{22}}{6\times 122\times 178\times 228}$$

Calculate 2316 to the power of 22 and get 105742168206643372768200770438011696592556515601531246649680432291335110656.

$$\frac{25\times 105742168206643372768200770438011696592556515601531246649680432291335110656}{6\times 122\times 178\times 228}$$

Multiply 25 and 105742168206643372768200770438011696592556515601531246649680432291335110656 to get 2643554205166084319205019260950292414813912890038281166242010807283377766400.

$$\frac{2643554205166084319205019260950292414813912890038281166242010807283377766400}{6\times 122\times 178\times 228}$$

Multiply 6 and 122 to get 732.

$$\frac{2643554205166084319205019260950292414813912890038281166242010807283377766400}{732\times 178\times 228}$$

Multiply 732 and 178 to get 130296.

$$\frac{2643554205166084319205019260950292414813912890038281166242010807283377766400}{130296\times 228}$$

Multiply 130296 and 228 to get 29707488.

$$\frac{2643554205166084319205019260950292414813912890038281166242010807283377766400}{29707488}$$

Reduce the fraction \frac{2643554205166084319205019260950292414813912890038281166242010807283377766400}{29707488} to lowest terms by extracting and canceling out 288.

$$\frac{9179007656826681663906316878299626440326086423744031827229204191956172800}{103151}$$

Factor

$$\frac{2 ^ {39} \cdot 3 ^ {20} \cdot 5 ^ {2} \cdot 193 ^ {22}}{19 \cdot 61 \cdot 89} = 8.898612380710494 \times 10^{67}\frac{87081}{103151} = 8.898612380710494 \times 10^{67}$$