sicp-all-tasks/sicp/1_002e43

Exercise 1.43: If 
  f
 is a numerical function
and 
  n
 is a positive integer, then we can form the 
  
    n
    
      th
    
  
 repeated
application of 
  f
, which is defined to be the function whose value at 
  x

is 
  
    f
    (
    f
    (
    …
    (
    f
    (
    x
    )
    )
    …
    )
    )
  
.  For example, if 
  f
 is the
function 
  
    x
    ↦
    x
    +
    1
  
, then the 
  
    n
    
      th
    
  
 repeated application of 
  f
 is
the function 
  
    x
    ↦
    x
    +
    n
  
.  If 
  f
 is the operation of squaring a
number, then the 
  
    n
    
      th
    
  
 repeated application of 
  f
 is the function that
raises its argument to the 
  
    
      2
      n
    
    -th
  
 power.  Write a procedure that takes as
inputs a procedure that computes 
  f
 and a positive integer 
  n
 and returns
the procedure that computes the 
  
    n
    
      th
    
  
 repeated application of 
  f
.  Your
procedure should be able to be used as follows:


((repeated square 2) 5)
625


Hint: You may find it convenient to use compose from Exercise 1.42.