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Simplify root(3)(a^(-2)).b xx root(3)(b^...

Simplify `root(3)(a^(-2)).b xx root(3)(b^(-2)).c root(3)(c^(-2)).a`.

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The correct Answer is:
`root(3)(abc)`
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CALCUTTA BOOK HOUSE-LAWS OF INDICES-EXERCISE - 6
  1. root(5)(x^8sqrt(x^8sqrt(x^(-8))))=

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  2. Find the value of (((8a^3)/(27x^(-3)))^(2/3)xx((64a^3)/(27x^(-3)))^(-2...

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  3. Simplify root(3)(a^(-2)).b xx root(3)(b^(-2)).c root(3)(c^(-2)).a.

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  4. If a^x=b,b^y =c,c^z=a, find the value of xyz.

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  5. Calculate : 9^(-3)xx((16)^(1/4))/(6^(-2))xx((1)/(27))^(-4/3).

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  6. If x^y=y^x, then prove that (x/y)^(x/y)=(x)^((x)/(y)-1).

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  7. Prove that (a^(3/2)+ab)/(ab-b^3)-(sqrt(a))/(sqrt(a)-b)=(sqrt(a))/(b).

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  8. Show that (x^(b-c))^((1)/(bc))xx(x^(c-a))^((1)/(ca))xx(x^(a-b))^((1)/(...

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  9. Factorise : (a+b).

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  10. Find the value of ((bc)^(b-c)(ca)^(c-a)(ab)^(a-b))/((a^(b-c)b^(c-a)c^(...

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  11. If p=a^x,q=a^y" and "a^2=(p^yq^x)^z, then find the value of xyz.

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  12. If a^(m^n)= (a^m)^n, then express m in terms of n.

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  13. If a^m a^n =a^(mn), then express m in terms of n.

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  14. If x=2,y=4, then what is the value of x+2y+sqrt((x-2y)^2)?

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  15. Which one is the greatest ? 3^(2^(2^2)), 3^(2.2.2), 3.2.2.2.

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  16. Find the value of root(3)(x^4sqrt(x^(-5)sqrt(x^6))).

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  17. Calculate : ((1)/(81))^(-5/4).

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  18. Calculate : {root(3)(4)xx(1)/(root(6)(8))xxroot(12)(2^(-1))}^(3/4).

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  19. Simplify : x^(1/3).x^(-1/4).x^(-1/2) divx^(-(7)/(12))

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  20. Simplify : root(4)(a^2b^3c^4)xxroot(3)(a^4b^6)xx(a^(1/2)b^(1/3)c^(1/4)...

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