Question

for any positive real number x find the value of [x power a / x power b ] power a+b [x power b / x power c ] power b+c [ x power c / x power a ] power c+a

Answer 1

Answer:

1

Step-by-step explanation:

${ (\frac{ {x}^{a} }{ {x}^{b} } )}^{a + b} . { (\frac{ {x}^{b} }{ {x}^{c} } )}^{b + c} .{ (\frac{ {x}^{c} }{ {x}^{a} } )}^{c + a}$

${( {x}^{a - b}) }^{a + b} .{( {x}^{b - c}) }^{b+ c}.{( {x}^{c - a}) }^{c + a}$

${x}^{(a - b)(a + b)} .{x}^{(b - c)(b+ c)}.{x}^{(c- a)(c+ a)}$

${x}^{( {a}^{2} - {b}^{2} )}.{x}^{( {b}^{2} - {c}^{2} )}.{x}^{( {c}^{2} - {a}^{2} )}$

${x}^{( {a}^{2} - {b}^{2} ) + ({b}^{2} - {c}^{2}) + ({c}^{2} - {a}^{2} )}$

${x}^{0} \: = 1$

Answer 2

Step-by-step explanation:

answer is 1

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