As n increases, the number of positive divisors of nxnxnxn.....n (n times) increases. Is it true or false?

Question

See the following table

Number    Number of positive divisors
1           1
2*2         3
3*3*3       4
4*4*4*4     9 

As n increases, the number of positive divisors of nxnxnxn.....n (n times) increases. Is it true or false?

Answer 1

False

because
5*5*5*5*5 6 (which is less than 9 from n = 4

how???

for 1........divisor is 1, so total 1
for 2*2 = 4 divisors are 1, 2 and 4, so total divisors are 3
for 3*3*3* = 27 divisors are 1,3,9 and 27, so total divisors are 4
for 4*4*4*4 = 256 divisors are 1, 2, 4, 8, 16, 32, 64, 128 and 256, so total divisors are 9

but
for 5*5*5*5*5 = 3125, divisors are 1, 5, 25, 125, 625 and 3125, so total divisors are 6