Question

2*2*2*2*2*2*3*3*3*3*3*4*4*4*4*5*5*5*5*6*6*6*6*7*7*7*7*8*8*8*9*9*9*9*1*1*1*1*1*2*2*2*2

Answer 1

Answer:

$\green { 2^{31}\times 3^{17}\times 5^{4} \times 7^{4}}$

Step-by-step explanation:

2*2*2*2*2*2*3*3*3*3*3*4*4*4*4*5*5*5*5*6*6*6*6*7*7*7*7*8*8*8*9*9*9*9*1*1*1*1*1*2*2*2*2

$= 2^{6} \times 3^{5} \times 4^{4} \times 5^{4} \times 6^{4} \times 7^{4} \times 8^{3} \times 9^{4} \times 2^{4}$

$= 2^{6} \times 3^{5} \times (2^{2})^{4} \times 5^{4} \times (2\times 3)^{4} \times 7^{4} \times (2^{3})^{3} \times (3^{2})^{4} \times 2^{4}$

$= 2^{6} \times 3^{5} \times 2^{8} \times 5^{4} \times 2^{4} \times \times 3^{4}\times 7^{4} \times 2^{9} \times 3^{8} \times 2^{4}$

$= 2^{6+8+4+9+4}\times 3^{5+4+8}\times 5^{4}\times 7^{4}$

$= 2^{31}\times 3^{17}\times 5^{4} \times 7^{4}$

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