Solve 2^{2}*5^{4}*4^{6}*10^{8}*6^{10}*15^{12}*8^14*20^16*10^18*25^20

$$2 ^ { 2 } \times 5 ^ { 4 } \times 4 ^ { 6 } \times 10 ^ { 8 } \times 6 ^ { 10 } \times 15 ^ { 12 } \times 8 ^ { 14 } \times 20 ^ { 16 } \times 10 ^ { 18 } \times 25 ^ { 20 }$$

Evaluate

$$210594726147627417600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 8 and 18 to get 26.

$$2^{2}\times 5^{4}\times 4^{6}\times 10^{26}\times 6^{10}\times 15^{12}\times 8^{14}\times 20^{16}\times 25^{20}$$

Calculate 2 to the power of 2 and get 4.

$$4\times 5^{4}\times 4^{6}\times 10^{26}\times 6^{10}\times 15^{12}\times 8^{14}\times 20^{16}\times 25^{20}$$

Calculate 5 to the power of 4 and get 625.

$$4\times 625\times 4^{6}\times 10^{26}\times 6^{10}\times 15^{12}\times 8^{14}\times 20^{16}\times 25^{20}$$

Multiply 4 and 625 to get 2500.

$$2500\times 4^{6}\times 10^{26}\times 6^{10}\times 15^{12}\times 8^{14}\times 20^{16}\times 25^{20}$$

Calculate 4 to the power of 6 and get 4096.

$$2500\times 4096\times 10^{26}\times 6^{10}\times 15^{12}\times 8^{14}\times 20^{16}\times 25^{20}$$

Multiply 2500 and 4096 to get 10240000.

$$10240000\times 10^{26}\times 6^{10}\times 15^{12}\times 8^{14}\times 20^{16}\times 25^{20}$$

Calculate 10 to the power of 26 and get 100000000000000000000000000.

$$10240000\times 100000000000000000000000000\times 6^{10}\times 15^{12}\times 8^{14}\times 20^{16}\times 25^{20}$$

Multiply 10240000 and 100000000000000000000000000 to get 1024000000000000000000000000000000.

$$1024000000000000000000000000000000\times 6^{10}\times 15^{12}\times 8^{14}\times 20^{16}\times 25^{20}$$

Calculate 6 to the power of 10 and get 60466176.

$$1024000000000000000000000000000000\times 60466176\times 15^{12}\times 8^{14}\times 20^{16}\times 25^{20}$$

Multiply 1024000000000000000000000000000000 and 60466176 to get 61917364224000000000000000000000000000000.

$$61917364224000000000000000000000000000000\times 15^{12}\times 8^{14}\times 20^{16}\times 25^{20}$$

Calculate 15 to the power of 12 and get 129746337890625.

$$61917364224000000000000000000000000000000\times 129746337890625\times 8^{14}\times 20^{16}\times 25^{20}$$

Multiply 61917364224000000000000000000000000000000 and 129746337890625 to get 8033551259904000000000000000000000000000000000000000000.

$$8033551259904000000000000000000000000000000000000000000\times 8^{14}\times 20^{16}\times 25^{20}$$

Calculate 8 to the power of 14 and get 4398046511104.

$$8033551259904000000000000000000000000000000000000000000\times 4398046511104\times 20^{16}\times 25^{20}$$

Multiply 8033551259904000000000000000000000000000000000000000000 and 4398046511104 to get 35331932090395930725974016000000000000000000000000000000000000000000.

$$35331932090395930725974016000000000000000000000000000000000000000000\times 20^{16}\times 25^{20}$$

Calculate 20 to the power of 16 and get 655360000000000000000.

$$35331932090395930725974016000000000000000000000000000000000000000000\times 655360000000000000000\times 25^{20}$$

Multiply 35331932090395930725974016000000000000000000000000000000000000000000 and 655360000000000000000 to get 23155135014761877160574331125760000000000000000000000000000000000000000000000000000000000.

$$23155135014761877160574331125760000000000000000000000000000000000000000000000000000000000\times 25^{20}$$

Calculate 25 to the power of 20 and get 9094947017729282379150390625.

$$23155135014761877160574331125760000000000000000000000000000000000000000000000000000000000\times 9094947017729282379150390625$$

Multiply 23155135014761877160574331125760000000000000000000000000000000000000000000000000000000000 and 9094947017729282379150390625 to get 210594726147627417600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000.

$$210594726147627417600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000$$

Factor

$$2^{124}\times 3^{22}\times 5^{98}$$