Question

Prove that (x^a/x^b)^c*(x^b/x^c)^a*(x^c/x^a)^b=1​

Answer 1

Step-by-step explanation:

$(\frac{ {x}^{a} }{ {x}^{b} } ) {}^{c} \times ({ \frac{ {x}^{b} }{ {x}^{c} }) }^{a} \times ({ \frac{ {x}^{c} }{ {x}^{a} } )}^{b} \\ \\ = ({x}^{a - b} ) {}^{c} \times ( {x}^{b - c} ) {}^{a} \times ({x}^{c - a} ) {}^{b} \\ \\ = {x}^{ac - bc} \times {x}^{ab - ac} \times {x}^{bc - ab} \\ \\ = {x}^{ac - bc + ab - ac + bc - ab} \\ \\ = {x}^{0} \\ \\ = 1 \: \: \: \: (proved) \\ \\ \\ \\ using \: formula \: \: \frac{ {x}^{m} }{ {x}^{n} } = {x}^{ m- n} \\ \\ ( {x}^{m}) {}^{n} = {x}^{mn} \\ \\ {x}^{m} \times {x}^{n} = {x}^{ m+ n} \\ \\ {x}^{0} = 1$