Solve 5left(47^15-197^14right)/7^16+37^15

$$\frac{ 5 \left( 4 { 7 }^{ 15 } -19 { 7 }^{ 14 } \right) }{ { 7 }^{ 16 } +3 { 7 }^{ 15 } }$$

Evaluate

$$\frac{9}{14}\approx 0.642857143$$

Solution Steps

Calculate 7 to the power of 15 and get 4747561509943.

$$\frac{5\left(4\times 4747561509943-19\times 7^{14}\right)}{7^{16}+3\times 7^{15}}$$

Multiply 4 and 4747561509943 to get 18990246039772.

$$\frac{5\left(18990246039772-19\times 7^{14}\right)}{7^{16}+3\times 7^{15}}$$

Calculate 7 to the power of 14 and get 678223072849.

$$\frac{5\left(18990246039772-19\times 678223072849\right)}{7^{16}+3\times 7^{15}}$$

Multiply 19 and 678223072849 to get 12886238384131.

$$\frac{5\left(18990246039772-12886238384131\right)}{7^{16}+3\times 7^{15}}$$

Subtract 12886238384131 from 18990246039772 to get 6104007655641.

$$\frac{5\times 6104007655641}{7^{16}+3\times 7^{15}}$$

Multiply 5 and 6104007655641 to get 30520038278205.

$$\frac{30520038278205}{7^{16}+3\times 7^{15}}$$

Calculate 7 to the power of 16 and get 33232930569601.

$$\frac{30520038278205}{33232930569601+3\times 7^{15}}$$

Calculate 7 to the power of 15 and get 4747561509943.

$$\frac{30520038278205}{33232930569601+3\times 4747561509943}$$

Multiply 3 and 4747561509943 to get 14242684529829.

$$\frac{30520038278205}{33232930569601+14242684529829}$$

Add 33232930569601 and 14242684529829 to get 47475615099430.

$$\frac{30520038278205}{47475615099430}$$

Reduce the fraction \frac{30520038278205}{47475615099430} to lowest terms by extracting and canceling out 3391115364245.

$$\frac{9}{14}$$

Factor

$$\frac{3 ^ {2}}{2 \cdot 7} = 0.6428571428571429$$