finding minimum order statistic of uniform distirbution

Question

I am trying to find the minimum of a uniform distribution of $Y_1 .. Y_n$ idd from 0 to theta

I understand how to derive it

$n(1-F_{y_1}(y))^{n-1}f_{y_1}$

But the solution says that it is the following

$\frac{n(1-\theta)^{n-1}}{\theta^n}$

And I don't understand where the $\theta^n$ in the denominator came from

Answer 1

So after looking over my math I realized why

$F_{y_1} = \int{\frac{1}{\theta}}$

So you would get $(1-\frac{1}{\theta})^{n-1}$

Simplify

$(\frac{\theta - y}{\theta})^{n-1}$

$\frac{(\theta-y)^{n-1}}{\theta^{n-1}}$