Question

Simplify:
$\frac{\left(x^{a+b}{)}^3\right(x^{b+c}{)}^3(x^{c+a}{)}^3}{(x^a{x}^b{x}^c{)}^6}$

Answer 1

$\frac{{\left(x^{a+b}\right)}^3{\left(x^{b+c}\right)}^3{\left(x^{c+a}\right)}^3}{{\left(x^a{x}^b{x}^c\right)}^6}$

$=\frac{{\left(x^{a+b}{x}^{b+c}{x}^{c+a}\right)}^3}{{\left(x^{a+b+c}\right)}^6}$

$=\frac{{\left(x^{a+b+b+c+c+a}\right)}^3}{x^{6(a+b+c)}}$

$=\frac{x^{6(a+b+c)}}{x^{6(a+b+c)}}$

$=1$