Question

$\frac{ {x}^{a(b - c)} }{ {x}^{b(a - c)} } \div ({ \frac{x {}^{b} }{x {}^{a} } })^{c} = 1$
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Answer 1

X*a(b-c)/xb (a-c) = 1 so this is your correct answer

Answer 2

Given :  $\dfrac{x^{a(b-c)}}{x^{b(a-c)}} \div (\dfrac{x^b}{x^a})^c$ = 1

To Find : Prove

Solution:

LHS =

$\dfrac{x^{a(b-c)}}{x^{b(a-c)}} \div (\dfrac{x^b}{x^a})^c$

(xᵃ)ᵇ = xᵃᵇ

xᵃ/xᵇ = xᵃ⁻ᵇ

=   $\dfrac{x^{ab-ac}}{x^{ba-bc}} \div \dfrac{x^{bc}}{x^{ac}}$

= $x^{ab-ac-(ba -bc)}} \div {x^{bc-ac}}$

= $x^{bc-ac}} \div {x^{bc-ac}}$

= 1

= RHS

$\dfrac{x^{a(b-c)}}{x^{b(a-c)}} \div (\dfrac{x^b}{x^a})^c$ = 1

QED

Hence proved

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