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Find the value of `((bc)^(b-c)(ca)^(c-a)(ab)^(a-b))/((a^(b-c)b^(c-a)c^(a-b))^(-1))`.

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If a = 1 , b = 2 , c = 3 , then find then value of (2a^(2)+2b^(2)+2c^(2)-ab-bc-ca)/(a^(3)+b^(3)+c^(3)-3abc)

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

(x^(b)/x^(c ))^(1/(bc))xx(x^(c )/x^(a))^(1/(ca))xx(x^(a)/x^(b))^(1/(ab))

Prove that ((a)/(b)-(b)/(c))^(3)+((b)/(c)-(c)/(a))^(3)+((c)/(a)-(a)/(b))^(3)=(3(ca-b^(2))(ab-c^(2))(bc-a^(2)))/(a^(2)b^(2)c^(2))

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If a,b,c are real positive numbers and theta =tan^(-1)[(a(a+b+c))/(bc)]^(1/2)+tan^(-1)[(b(a+b+c))/(ca)]^(1/2)+tan^(-1)[(c(a+b+c))/(ab)]^(1/2) , then tantheta equals

|{:(a^2,a^2-(b-c)^2,bc),(b^2,b^2-(c-a)^2,ca),(c^2,c^2-(a-b)^2,ab):}|=(a-b)(b-c)(c-a)(a+b+c)(a^2+b^2+c^2)

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CALCUTTA BOOK HOUSE-LAWS OF INDICES-EXERCISE - 6
  1. Show that (x^(b-c))^((1)/(bc))xx(x^(c-a))^((1)/(ca))xx(x^(a-b))^((1)/(...

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  2. Factorise : (a+b).

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

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

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

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

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

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

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

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

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

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

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  13. 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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  14. Simplify : {(a)^(n^(2)-1)}^((n)/(n+1))xx(sqrt(a^(2n)))/(a).

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  15. Simplify : ((p+(1)/(q))^m(p-(1)/(q))^n)/((q+(1)/(p))^m(q-(1)/(p))^n).

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  16. Simplify : (2^n.6^(m+1).10^(m-n).15^(m+n-2))/(4^m.3^(m+n).25^(m-1)).

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  17. Simplify : (x^((b+c)/(c-a)))^((1)/(a-b))xx(x^((c+a)/(a-b)))^((1)/(b-c)...

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  18. Simplify : (a+b)^mxx(a-b)^mxx(a^2+b^2)^m.

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  19. Simplify : ({(a^m)^(1/r)(a^q)^(1/n)}^(nr))/({root(q)(b^n)(root(m)(b))^...

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  20. Simpify : (1)/((4x^3-3x)^2)-{((3sqrt(1-x^2))/(x)-((1-x^2)^(3/2))/(x^3)...

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