Question

Pls solve 7th question

Answer 1

Answer:

$\displaystyle\frac{x^{a(b-c)}}{x^{b(a-c)}}\div\left(\frac{x^b}{x^a}\right)^c\\ \\=\frac{x^{ab-ac}}{x^{ba-bc}}\div\frac{(x^b)^c}{(x^a)^c}\\ \\=\frac{x^{ab-ac}}{x^{ba-bc}}\div\frac{x^{bc}}{x^{ac}}\\ \\=\frac{x^{ab-ac}}{x^{ba-bc}}\times\frac{x^{ac}}{x^{bc}}\\ \\=\frac{x^{ab-ac}\,\times\,x^{ac}}{x^{ba-bc}\,\times\,x^{bc}} \\ \\=\frac{x^{ab-ac+ac}}{x^{ba-bc+bc}} \\ \\=\frac{x^{ab}}{x^{ba}} \\ \\=\frac{x^{ab}}{x^{ab}} \\ \\=1$