2022-06-24

simplify fractions with exponent
The given fraction is: $\left(\frac{a}{b}{\right)}^{n}\cdot \left(\frac{b}{c}{\right)}^{n}\cdot \left(\frac{c}{a}{\right)}^{n+1}$
The given solution is: $\frac{c}{a}$
What I have done so far:
$\left(\frac{a}{b}{\right)}^{n}\cdot \left(\frac{b}{c}{\right)}^{n}\cdot \left(\frac{c}{a}{\right)}^{n+1}$ | multiply $\frac{a}{b}$ and $\frac{b}{c}$ because of same exponent
$\left(\frac{ab}{bc}{\right)}^{n}\ast \left(\frac{c}{a}{\right)}^{n+1}$ | get rid of $b$
$\left(\frac{a}{c}{\right)}^{n}\ast \left(\frac{c}{a}{\right)}^{n+1}$
Can you please explain how I continue simplifying or what I did wrong? Thanks!

Alisa Gilmore

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

boloman0z

You're almost there:
Note that:
${\left(\frac{c}{a}\right)}^{n+1}={\left(\frac{c}{a}\right)}^{n}{\left(\frac{c}{a}\right)}^{1}$
${\left(\frac{abc}{abc}\right)}^{n}\frac{c}{a}$