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\(16\div\frac14\\~\\16\times\frac41\\~\\16\times4\\~\\64\)

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\(\frac{16}{\frac{1}{4}}=64\). In factor form, \(64=2^6\)

 

 

 

 

\(\frac{16}{\frac{1}{4}}\)

 

This is the original expression given, or, at least, this was my interpretation. If it is wrong, please correct me. Dividing a number by a fraction is the same as multiplying a number by that fraction's reciprocal:

 

\(\frac{16}{\frac{1}{4}}=16*\frac{4}{1}=64\)

 

You said that you wanted your answer in factor form. Continue creating a tree of factors until you get down to prime numbers:

 

64

/\

8   *   8

/\         /\

2 * 4    4 * 2

               /\     /\                

2*2   2*2

 

Combine the bolded numbers, and you are done! There are 6 2's. 

\(2*2*2*2*2*2=2^6\)