Powers

Express the expression
1000211010110145 { 1000 } ^ { 21} \cdot { 10 } ^ { 101} \cdot { 10 } ^ { 145}
as the n-th power of the base 10.

Result

n =  309

Solution:

1000211010110145=10101+145(103)21  n=101+145+213=309 { 1000 } ^ { 21} \cdot { 10 } ^ { 101} \cdot { 10 } ^ { 145} = { 10 } ^ { 101 + 145} \cdot ({ 10}^ 3 )^{ 21} \ \\ \ \\ n = 101+145 + 21\cdot 3 = 309



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