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Simplify : ((x^a)/(x^b))^(a^2+b^(2+a b))...

Simplify : `((x^a)/(x^b))^(a^2+b^(2+a b))xx((x^b)/(x^c))^(b^2+c^(2+b c))+((x^c)/(x^a))^(c^2+a^(2+c a))`

A

1

B

`-1`

C

0

D

None of these

Text Solution

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The correct Answer is:
A
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Simplify :((x^(a))/(x^(b)))^(a^(2)+b^(2)+ab)xx((x^(b))/(x^(c)))^(b^(2)+c^(2)+bc)xx((x^(c))/(x^(a)))^(c^(2)+a^(2))

Simplify: ((x^(a))/(x^(-b)))^(a-b)xx((x^(b))/(x^(-c)))^(b-c)xx((x^(c))/(x^(-a)))^(c-a)

Knowledge Check

  • The value ((x^a)/(x^b))^((a^2 + ab + b^2)) ((x^b)/(x^c))^((b^2 + bc + c^2))((x^c)/(x^a))^((c^2 + ca + a^2)) is :

    A
    `-1`
    B
    `x^(abc)`
    C
    `1`
    D
    `x^(a +b + c)`

  • Simplify : ((x^a)/(x^b))^(4)xx((x^b)/(x^c))^(3)xx((x^c)/(x^a))^2

    A
    `0`
    B
    `x`
    C
    `1`
    D
    `x^(2a-b-c)`

  • ((x^(a))/(x^(b)))^(a^(2)+ab+b^(2))((x^(b))/(x^(c )))^(b^(2)+bc+c^(2))((x^(c ))/(x^(a)))^(c^(2)+ca+a^(2))=?

    A
    `3`
    B
    `2`
    C
    `1`
    D
    `0`

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