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

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

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

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

In each of the following cases show that (dy).(dx)=0 , when y = (x^(1/(c-a)))^(1/(b-a))xx(x^(1/(a-b)))^(1/(c-b))xx(x^(1/(b-c)))^(1/(a-c))

Simply (x^(1/(a-b)))^(1/(a-c))xx(x^(1/(b-a)))^(1/(b-c))xx(x^(1/(c -a)))^(1/(c-b))

If a+b+c =0 Prove that root(bc)(x^(a^(2))/x^(bc))xxroot(ca)(x^(b^(2))/x^(ca))xxroot(ab)(x^(c^(2))/x^(ab))=1

Show that ((x+b)(x+c))/((b-a)(c-a))+((x+c)(x+a))/((c-b)(a-b))+((x+a)(x+b))/((a-c)(b-c))=1 is an identity.

If x^(a).x^(b).x^(c )=1 (x ne 0) show that x^(a^(2)/(bc)).x^(b^(2)/(ca)).x^(c^(2)/(ab))=x^(3)

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

(1)/(1+x^(a-b)+x^(a-c))+(1)/(1+x^(b-c)+x^(b-a))+(1)/(1+x^(c-a)+x^(c-b))

Show that (1)/(log_(a)bc+1)+(1)/(log_(b)ca+1)+(1)/(log_(c )ab+1)=1

CALCUTTA BOOK HOUSE-LAWS OF INDICES-EXERCISE - 6
  1. If x^y=y^x, then prove that (x/y)^(x/y)=(x)^((x)/(y)-1).

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

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

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  4. Factorise : (a+b).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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