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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

Verified by Experts

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))

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 :

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

Prove that: ((x^(a))/(x^(b)))^(a)-2+ab+b^(2)x((x6b)/(x^(c)))^(b)-2+bc+c^(2)x((x^(c))/(x^(a)))^(c)-2+ca+a^(2)

Assuming that x is a positive real number and a,b,c are rational numbers,show that: ((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)=1

((x^(a))/(x^(-b)))^(a^(2)-ab+b^(2))times((x^(b))/(x^(-c)))^(b^(2)-bc+c^(2))times((x^(c))/(x^(-a)))^(c^(2)-ca+a^(2))

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`
    • S CHAND IIT JEE FOUNDATION-POWERS AND ROOTS -UNIT TEST-1
    1. Simplify : ((x^a)/(x^b))^(a^2+b^(2+a b))xx((x^b)/(x^c))^(b^2+c^(2+b c)...

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    2. Which one of the following is correct? The number 222222 is :

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    3. In a division operation, the divisor is 5 times the quotient and twice...

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    4. LCM of two numbers is 16 times their HCF. The sum of LCM and HCF is 85...

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    5. Find the value of sqrt((0. 289)/(0. 00121)) .

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    6. Consider the following statements : A number a(1)a(2)a(3)a(4)a(5) is...

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    7. A bell rings every 5 seconds. A second bell rings every 6 seconds and ...

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    8. if 4^x-4^(x-1)=24 then the value of (2x)^x equals:

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    9. The first twenty natural numbers from 1 to 20 are written next to each...

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    10. x, y and z are the natural numbers. Which of the following statements ...

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    11. The number of prime factors in ((1)/(6))^(12)xx(8)^(25)xx((3)/(4))^(...

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    12. The value of 2/3xx3/(5/6-:2/3\ of\ 1 1/4) is 1/2 (b) 2/3 (c) 1 (d) ...

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    13. If ((1)/(5))^(3y)=0.008, then the value of (0.25)^(y//2) will be

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    14. Simplify : [root(3)root(6)(5^(9))]^(4)[root(3)root(6)(5^(9)]]^(4)

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    15. The value of 0.1bar7 is

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    16. The least values of x and y so that 7x342y is divisible y 88 are

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    17. The total number of 8 digit numbers is

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    18. If X, Y are positive real numbers such that XgtY and A is any positive...

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    19. Assertion (A) : The number 90356294 is divisible by 4. Reason (R ) :...

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    20. Given two different prime numbers P and Q, find the number of divisors...

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