Question

Find the simplified form of the following:
$\frac{(x^{a+b}{)}^3\times (x^{b+c}{)}^3\times (x^{c+a}{)}^3}{(x^a\times x^b\times x^c{)}^6}$

Answer 1

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

$=\frac{x^{(3a+3b)}.x^{(3b+3c)}.x^{(3a+3c)}}{x^{(6a+6b+6c)}}\left[\right(a^m{)}^n=a^{mn}]$

$=\frac{x^{3a+3a+3b+3b+3c+3c}}{x^{6a+6b+6c}}[a^m\times a^n=a^{m+n}]$

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

$=x^{(6a+6b+6c)-(6a+6b+6c)}[a^m÷a^n=a^{m-n}]$

$=x^{6a+6b+6c-6a-6b-6c}$

$=x^{\circ }$

$=1$