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(i) Simplify (2^(2/3)-2^((-2)/3))(2^(4/3...

(i) Simplify `(2^(2/3)-2^((-2)/3))(2^(4/3)+1+2^((-4)/3))`
(ii) `[(root(6)(7))^(2)+(root(6)(7))^(-2)][(root(6)(7))^(4)-1+(root(6)(7))^(-4)]`

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Verified by Experts

The correct Answer is:
`(50)/(7)`
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PEARSON IIT JEE FOUNDATION-INDICES-Test Your Concepts (Short Answer Type Questions)
  1. Simplify (5(81)^(n+1)-3^(4n+5))/(3xx3^(4n)+(81)^n).

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  2. (1) If 5^(n+2)=625 ,f i n d[(n+3)]^(1/3): (2) If (32/243)^n=8/27 ,f i...

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  3. If ((32)/(243))^(n)= (8)/(27), then find ((n+0.4)/(1024))^(-n)

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  4. simplify (2^(2/3)-2^(- 2/3))(2^(4/3)+1+2^(- 4/3))

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  5. (i) Simplify (2^(2/3)-2^((-2)/3))(2^(4/3)+1+2^((-4)/3)) (ii) [(root(...

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  6. If 16200=2^(a)xx3^(b)xx^(c), then find a, b, c.

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  7. Simplify ((p^(a))/(p^(b))) xx ((p^(b))/(p^(c ))) xx ((p^(c ))/(p^(a)))...

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  8. If [root(9)((2/3)^5)]^(sqrt(x-5)) = a^0, find the value of x.

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  9. Simplify ((p^(a+b))^(5).(p^(b+c))^(5).(p^(c+a))^(5))/((p^(a). p^(b). p...

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  10. If 5^(3x+2)=25xx5^((4x-1)), find the value of x.

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  11. Which of the following is greater between each of the two numbers ? ...

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  12. Which of the following is greater between each of the two numbers ? ...

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  13. Which of the following is greater between each of the two numbers ? ...

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  14. If 5^x=3^y=45^z, prove that 1/z=1/x+2/y.

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  15. Prove that 1/(1+p+q^(- 1))+1/(1+q+r^(- 1))+1/(1+r+p^(- 1))=1,if pqr=1 ...

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  16. ((a+b+c)^(a+b)(a+b+c)^(b+c)(a+b+c)^(c+a))/([(a+b+c)^(a) (a+b+c)^(b) (a...

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  17. Simplify the given expressions (a^(p+q))^(p-q) (a^(q+r))^(q-r) (a^(r...

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  18. [(a/b)^(sqrt(p)+sqrt(q))]^(sqrtp-sqrtq)[(a/b)^(sqrt(q)+sqrt(r))]^(sqrt...

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  19. Prove that ((x^(-1)+y^(-1))/x^(-1))^(-1)+((x^(-1)-y^(-1))/x^(-1))^(...

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  20. If a, b, c are real numbers, then show that root(5)(ab^-1)xxroot( 5)...

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