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If `x` is a positive real number and the exponents are rational numbers, show that: `((x^a)/(x^b))^(a+b-c)\ ((x^b)/(x^c))^(b+c-a)((x^c)/(x^a))^(c+a-b)=1`

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RS AGGARWAL-NUMBER SYSTEMS-Exercise 1G
  1. Simplify (i) 2^((2)/(3)) xx 2^((1)/(3)) (ii) 2^((2)/(3)) xx 2^((1...

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  2. Simplify (i) (6^(1//4))/(6^(1//5)) (ii) (8^(1//2))/(8^(2//3)) (iii)...

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  3. Simplify (i) 3^((1)/(4)) xx 5^((1)/(4)) (ii) 2^((5)/(8)) xx 3^((5)/(...

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  4. Simplify (i) (3^(4))^((1)/(2)) (ii) (64)^((1)/(6)) (iii) ((1)/(3^(4)...

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  5. Evalute (i) (125)^((1)/(3)) (ii) (64)^((1)/(6)) (iii) (25)^((3)...

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  6. If a=2, b= 3 find the values of (a^(b) + b^(a))^(-1) (ii) (a^(a...

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  7. Simplify (i) ((81)/(49))^(-(3)/(2)) (ii) (14641)^(0.25) (iii) ((32...

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  8. Simplify: 4/((216)^(-2/3))+1/((256)^(-3/4))+2/((243)^(-1/5))

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  9. Evaluate (i) (1^(3) + 2^(3) + 3^(3))^((1)/(2)) (ii) [5(8^((1)/(2))...

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  10. Prove that . (i) [8^(-(2)/(3)) xx 2^((1)/(2))xx 25^(-(5)/(4))] div[...

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  11. Simplify root(4)root(3)(x^(2)) and express the result in the exponen...

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  12. The product root3(2).root4(2). root12(32) equal to

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  13. Simplify. (i) ((15^(1//3))/(9^(1//4)))^(-6) (ii) ((12^(1//5))/(27^(...

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  14. Find the value of x in each of the following . (i) root5(5x + 2) =...

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  15. Prove that. (i) sqrt(x^(-1) y) .sqrt(y^(-1) z) . Sqrt(z^(-1) x) = 1...

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  16. If x is a positive real number and the exponents are rational numbe...

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  17. If (9^(n)xx3^(2)xx(3^(-n//2))^(-2)-(27)^(n))/(3^(3m)xx2^(3))=(1)/(27),...

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  18. Write the following in ascending order of magniude . root(6)(6),...

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