Complete the analogy:
$$145:15^4::532:?$$

Let's decipher the relation in the first pair: $145:15^4$
The digits of the first number are $1$, $4$, and $5$.
Look at how these digits are rearranged to form the expression $15^4$:

* The first digit ($1$) becomes the tens digit of the base.
* The third digit ($5$) becomes the units digit of the base.
* The middle digit ($4$) becomes the exponent (power).

So, $\text{Digits}(XYZ)\to X{Z}^Y$

Now, applying this identical rule to the second number $532$:

* $X=5$
* $Y=3$
* $Z=2$

Forming the expression $X{Z}^Y$:

$$\text{Base}=XZ=52$$

$$\text{Exponent}=Y=3$$

Thus, the result is $52^3$.