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Question
Show that:
`[{x^(a(a-b))/x^(a(a+b))}div{x^(b(b-a))/x^(b(b+a))}]^(a+b)=1`
Solution
`[{x^(a(a-b))/x^(a(a+b))}div{x^(b(b-a))/x^(b(b+a))}]^(a+b)=1`
LHS = `[{x^(a(a-b))/x^(a(a+b))}div{x^(b(b-a))/x^(b(b+a))}]^(a+b)`
`=[{x^(a(a-b))/x^(a(a+b))}xx{x^(b(b+a))/x^(b(b-a))}]^(a+b)`
`=[{x^(a^2-ab)/x^(a^2+ab)}xx{x^(b^2+ab)/x^(b^2-ab)}]^(a+b)`
`=[{x^(a^2-ab-a^2-ab)}xx{x^(b^2+ab-b^2+ab)}]^(a+b)`
`=[x^(-2ab)xx x^(2ab)]^(a+b)`
`=[x^(-2ab+2ab)]^(a+b)`
`=[x^0]^(a+b)`
= 1
= RHS
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