Answer
$$\frac{a}{n}
$$
Work Step by Step
We know that:
$$
f^{\prime}(x)=nx^{n-1}
$$
Then at $x=a, m=f^{\prime}(a)=na^{n-1},$ hence the tangent line is
$$
\begin{aligned}
\frac{y-y_{1}}{x-x_{1}} &=m \\
\frac{y-a^n}{x-a} &=na^{n-1} \\
y &=na^{n-1} (x-a)+a^n
\end{aligned}
$$
since the tangent line intersect with $x-$ axis at $x=0,$ then $Q$ has coordinates $(a-\frac{a}{n},0), R$ has coordinates $(c,0)$ and the subtangent is
$$
a-\left(a-\frac{a}{n}\right)=\frac{a}{n}
$$
