The largest doll is 12 inches tall. the height of each of the other dolls is 710710 the height of the next larger doll. write an expression involving a power for the height of the smallest doll. then evaluate the expression to find the height of the smallest doll to the nearest tenth of an inch.

the question doesn't say how many dolls. there would be an infinite number.  
But we'll just form the equation for the nth doll.     
 Largest doll = 12 inches
 2nd doll = (12) x 0.7
 3rd doll = (12 x 0.7) x 0.7
 4th doll = [(12 x 0.7) x 0.7) x 0.7 
  
 OK, We now see the pattern. Each successive doll is mult by the previous

doll height x 0.7
 the Nth doll, 12 is mult by 0.7(n-1)  
 So, the height of the nth doll can be expressed as: 12 x 0.7(n-1)  
 example: 4th doll = 12 x 0.7(4-1) = 12 x 0.73
  10th doll = 12 x 0.7(10-1) = 12 x 0.79 etc