Question

Prove that :
`[ x^(a(b - c))]/[x^b(a - c)] ÷ ((x^b)/(x^a))^c = 1`

Answer 1

We need to prove that
`[ x^(a(b - c))]/[x^b(a - c)] ÷ ((x^b)/(x^a))^c = 1`

LHS =

= `x^[a(b - c ) - b( a - c )] ÷ x^(bc)/x^(ac)` 

= `x^( ab - ac - ab + bc ) ÷ x^( bc - ac )`

= `x^( ab - ac - ab + bc - bc + ac )`
= `x^0`
= 1
= RHS