## Calculus (3rd Edition)

$$\frac{a}{n}$$
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 $$a-\left(a-\frac{a}{n}\right)=\frac{a}{n}$$