दर्शाइये:
(i) `(x^(a(b-c)))/(x^(b(a-c)))div((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

(i) `(x^(a(b-c)))/(x^(b(a-c)))div((x^(b))/(x^(a)))^(c)`
`=(x^(ab-ac))/(x^(ba-bc))div(x^(b-a))^(c)`
`=x^((ab-ac)-(ba-bc))xx1/(x^((b-a)c))`
`=x^(ab-ac-ba+bc)xx1/(x^(bc-ac))=x^(-ac+bc).x^(ac-bc)=x^(-ac+bc+ac-bc)=x^(0)=1`
(ii) `((x^(a+b))^(2)(x^(b+c))^(2)(x^(c+a))^(2))/((x^(a)x^(b)x^(c))^(4))`
`=(x^(2(a+b)).x^(2(b+c))x^(2(c+a)))/((x^(a))^(4)(x^(b))^(4)(x^(c))^(4))`
`=(x^(2a+2b).x^(2b+2c).x^(2c+2a))/(x^(4a).x^(4b).x^(4c))=(x^(2a+2b+2b+2c+2c+2a))/(x^(4a+4b+4c))=(x^(4a+4b+4c))/(x^(4a+4b+4c))=1`