Question

[(x^a/x^b)^1/a*b]*[(x^b/x^c)^1/b*c]*[(x^c/x^a)*1/a*c]=1

Answer 1

Answer:

Step-by-step explanation:

Given :

To prove :

$(\frac{x^a}{x^b} )^{\frac{1}{ab} } * (\frac{x^b}{x^c} )^{\frac{1}{bc} }*(\frac{x^c}{x^a})^{\frac{1}{ac} } = 1$

Proof :

LHS = $(\frac{x^a}{x^b} )^{\frac{1}{ab} } * (\frac{x^b}{x^c} )^{\frac{1}{bc} }*(\frac{x^c}{x^a})^{\frac{1}{ac} }$

= $\sqrt[ab]{ { (\frac{x^a}{x^b} ) }}* \sqrt[bc]{(\frac{x^b}{x^c} ) }}*\sqrt[ac]{(\frac{x^c}{x^a})}$

= $\frac{x^{\frac{a}{ab} }}{x^{\frac{b}{ab} }} * \frac{x^{\frac{b}{bc} }}{x^{\frac{c}{bc} }} * \frac{x^{\frac{c}{ac} }}{x^{\frac{a}{ac} }}$

= $\frac{x^{\frac{1}{b} }}{x^{\frac{1}{a} }} * \frac{x^{\frac{1}{c} }}{x^{\frac{1}{b} }} * \frac{x^{\frac{1}{a} }}{x^{\frac{1}{c} }}$

= 1

Answer 2

Answer:

Solve 1: x^0 = 1

Step-by-step explanation:

Refer to the attachment ^^