((1^m)/(5^m))((1^16)/(4^16)) = 1/(2(10)^31)
What is m?  Choose one:  A) 17  B) 18  C) 34  D) 31  E) 36

Rationale: ( ( 1 ^ m ) / ( 5 ^ m ) ) ( ( 1 ^ 16 ) / ( 4 ^ 16 ) ) = 1 / ( 2 ( 10 ) ^ 31 ) ( ( 1 / 5 ) ^ m ) * ( ( 1 / 2 ) ^ 32 ) = 1 / ( 2 * ( 2 * 5 ) ^ 31 ) ) 2 ^ 36 will cancel out , since 1 can be written as 1 ^ 35 , so ( 1 / 5 ) ^ m = ( 1 / 5 ) ^ 31 ( ( 1 / 5 ) ^ m ) * ( ( 1 / 2 ) ^ 32 ) = 1 / [ ( 2 ^ 32 ) * ( 5 ^ 31 ) ] so , m = 31 answer d
Answer: D