7 (6) + 14!!! And this needs to be 20 characters long so I’m adding this

Now, If the exponent was negative like you asked....
Since she has seven key the probability that the first one will open the door is

if it takes three attempts to open the door,the probability is

if the three attempts would not work
then the probability that the fourth attempt will open the door is

hope this helps
Simple, first change the 4.5% into 0.045
Thus,
900=0.045*n
900/0.045=0.045n/0.045
20,000=n
Thus, your answer is 20,000.