Question

For any positive real number x, write the value of

${\left\{\right(x^a{)}^b\}}^{\frac{1}{ab}}{\left\{\right(x^b{)}^c\}}^{\frac{1}{bc}}{\left\{\right(x^c{)}^a\}}^{\frac{1}{ca}}$

Answer 1

${\left\{\right(x^a{)}^b\}}^{\frac{1}{ab}}{\left\{\right(x^b{)}^c\}}^{\frac{1}{bc}}{\left\{\right(x^c{)}^a\}}^{\frac{1}{ca}}={\left(x^{ab}\right)}^{\frac{1}{ab}}.{\left(x^{bc}\right)}^{\frac{1}{bc}}.{\left(x^{ca}\right)}^{\frac{1}{ca}}=x^{\frac{ab}{ab}}.x^{\frac{bc}{bc}}.x^{\frac{ca}{ca}}=x^1\times x^1\times x^1=x\times x\times x=x^3$