simplify fractions with exponent

Question

The given fraction is: $(\frac{a}{b})^n \cdot (\frac{b}{c})^n \cdot (\frac{c}{a})^{n+1}$

The given solution is: $\frac{c}{a}$

What I have done so far:

$(\frac{a}{b})^n \cdot (\frac{b}{c})^n \cdot (\frac{c}{a})^{n+1}$ | multiply $\frac{a}{b}$ and $\frac{b}{c}$ because of same exponent

$(\frac{ab}{bc})^n * (\frac{c}{a})^{n+1}$ | get rid of $b$

$(\frac{a}{c})^n * (\frac{c}{a})^{n+1}$ | ??

Can you please explain how I continue simplifying or what I did wrong? Thanks!

Answer 1

You're almost there:

Note that:

$$ \left(\frac{c}{a}\right)^{n+1} = \left(\frac{c}{a}\right)^n\left(\frac{c}{a}\right)^1$$

Your expression becomes:

$$ \left(\frac{abc}{abc}\right)^n \frac{c}{a}$$

Does that help?

Answer 2

$$(\frac{a}{b})^n \cdot (\frac{b}{c})^n \cdot (\frac{c}{a})^{n+1}=$$ $$\frac{a^n}{b^n} \cdot \frac{b^n}{c^n} \cdot \frac{c^{n+1}}{a^{n+1}}=$$ $$\frac{a^nb^nc^{n+1}}{b^nc^na^{n+1}}=$$ $$\frac{a^nb^nc}{b^na^{n+1}}=$$ $$\frac{b^nc}{b^na}=$$ $$\frac{c}{a}$$