Question

By what number should we multiply 2 to power -5 so that the product may be equal to 2 to the power -1

Answer 1

Let the required number be K,



Given, Product of K and 2^( - 5 ) is equal to 2^( - 1 )

=> 2^( - 5 ) × k = 2^( - 1 )



$= > K = \frac{ {2}^{ - 1} }{ {2}^{ - 5} } \\ \\ \\ => K = {2}^{ - 1 - ( - 5)} \\ \\ \\ = > K = {2}^{ - 1 + 5} \\ \\ \\ => K = {2}^{4}$




Hence, Required number is 2⁴

Answer 2

Let the required number be a,



Given, Product of a and 2^( - 5 ) is equal to 2^( - 1 ) 

=> 2^( - 5 ) × a = 2^( - 1 ) 

$=> x = \frac{ {2}^{ - 1} }{ {2}^{ - 5} } \\ \\ => x = {2 }^{ - 1 + 5} \\ \\ = > x = {2}^{4}$





The number by which is should be multiplied is 2⁴ or 16