Question

prove it .please help me it is urgent.i will thanks you and mark you as brainliest​

Answer 1

${x}^{ \frac{1}{(a - b)( a- c)} } . {x}^{ \frac{1}{( b-c )(b - a)} } . {x}^{ \frac{1}{( c- a)( c-b )} } \\ = > {x}^{\frac{1}{(a - b)( a- c)} +\frac{1}{( b-c )(b - a)} + \frac{1}{( c- a)( c-b )} } \\ \red{taking \: lcm} \\ = > {x}^{ \frac{(c - b) + ( a-c ) + (b - a)}{( a-b )( b- c)(c -a )} } \\ = > {x}^{ \frac{0}{( a-b )( b- c)(c -a )} } \\ \boxed{= > {x}^{0} = 1}$

$\green{formulae} \\ = > {( {x}^{a} )}^{b} = {x}^{ab} \\ = > {x}^{a} . {x}^{b} = {x}^{a +b } \\ = > {x}^{0} = 1$

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