Select the related word/letters/number from the given alternatives.
8 : 9 :: 25 : ?

Let us look at the pattern of squares and cubes:
First term: 8=2
3


Second term: 9=3
2
=(2+1)
2


Now apply this pattern to the third term:

Third term: 25=5
2


Following the base progression (x
3
:(x+1)
2
), we need to look closely at the configuration. Here, the first set is 2
3
:3
2
. The second set begins with a square, 5
2
.

Alternatively, the relationship can be viewed as consecutive bases with exponents alternating:
2
3
:3
2

5
2
:6
1
=6 (Not in options)

Let's look at a simpler base-exponent combination:
8=2
3

9=3
2

25=5
2

The pattern is x
3
:(x+1)
2
. For 25, it is 5
2
. Let's test the consecutive power sequence:
2
3
=8
3
2
=9
5
2
=25
6
1
=6 (Not in options)

Let's look at another square/cube pattern:
8=2
3

9=3
2

25=5
2

The matching element could follow the prime base progression, or simply standard exponent matching. Another classic approach:
8→2
3
, then next is (2+1)
2
=9.
If the second pair starts with 5
2
=25, the next term following the cross pattern x
y
:y
x
is not applicable.
Let's look at the options: 32=2
5
.
If the pattern is x
3
:(x+1)
2
, then for the next set we have y
2
:(y+1)
x
or similar.
Let's see: 2
3
:3
2
(bases are 2,3; exponents are 3,2).
Next pair: 5
2
:2
5
=32 (bases are 5,2; exponents are 2,5). This is the inverted base-exponent rule (a
b
:b
a
).

2
3
=8 and 3
2
=9

5
2
=25 and 2
5
=32
Therefore, the missing number is 32.