Show that: `(i) (x^(a(b-c)))/(x^(b(a-c)))-:((x^b)/(x^a))^c=1,` `(ii) ((x^(a+b))^2\ (x^(b+c))^2\ (x^(c+a))^2)/((x^a\ x^b x^c)^4)=1`

Explanation

1:`(x^a(b-c))/(x^b(a-c))-:((x^b)/(x^a))^c=1`
`=(x^(ab-ac))/(x^(ab-bc))-:((x^(bc))/(x^(ac)))`
`=(x^(ab-ac))/(x^(ab-bc))xx(x^(ac))/(x^(bc))`
`=(x^(ab-ac+ac))/(x^(ab-bc+bc))`
`=(x^(ab))/(x^(ab))=1`
2:`((x^(a+b))^2\ (x^(b+c))^2\ (x^(c+a))^2)/((x^a\ x^b x^c)^4)=1`
`=((x^a.x^b)^2\(x^b.x^c)^2\(x^c.x^a)^2)/((x^ax^bx^c)^4)`
`=(x^(2a).x^(2b).x^(2a).x^(2c).x^(2c).x^(2a))/(x^ax^bx^c)^4`
`=(x^(4a)x^(4b)x^(4c))/(x^ax^bx^c)^4`
`=((x^ax^bx^c)^4)/((x^ax^bx^c)^4)`
`=1`