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

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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))

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)) .

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

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

Simply x^(a-b).x^(b-c).x^(c-a)

If (1)/(a)+(1)/(c )=(1)/(2b-a)+(1)/(2b-c) , then

Simplify : {(x^(a+b-c) xx x^(a-b+c))^b}^c .

If F(x)=((x-b)(x-c))/((a-b)(a-c))+((x-c)(x-a))/((b-c)(b-a))+((x-a)(x-b))/((c-a)(c-b)) , show that F(0)=1.

Simplify : ((x^a)/(x^b))^(a^2+ab+b^2)xx((x^b)/(x^c))^(b^2+bc+c^2)xx((x^c)/(x^a))^(c^2+ca+a^2) .

CHHAYA PUBLICATION-LAWS OF INDICES-Short Answer Type Questions
  1. Simply (x^(m)/x^(n))^(m^(2)+mn+n^(2))xx(x^(n)/x^(l))^(n^(2)+nl+l^(2...

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  2. Simply (a^(p)/a^(q))^(p+q-r).(a^(q)/a^(r ))^(q+r-p).(a^(r )/a^(p))^...

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

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  4. Simply (x^(p)/x^(q))^(p+q)div((x^(p+q))/(x^(p-q)))^(p^(2)/(q))

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  5. Prove (1/(1+x^(b-a)+x^(c-a)))+(1/(1+x^(a-b)+x^(c-b)))+(1/(1+x^(a-c)+...

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  6. Prove root(p+q)(x^(p^(2))/(x^(q^(2))))xxroot(q+r)(x^(q^(2))/(x^(r^(2...

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  7. Prove root(ln)((x^(l))/(x^(n)))xxroot(nm)((x^(n))/(x^(m)))xxroot(ml)...

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  8. If x=2^(2/3)+2^(1/3) show that x^(3)-6x=6

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  9. If a=2^(1/3)-2^(-1/3) show that 2a^(3)+6a-3=0

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  10. If x=2+2^(2/3)+2^(1/3) show that x^(3)-6x^(2)+6x-2=0

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  11. If x^(1/a)=y^(1/b)=z^(1/c ) and xyz =1 show that a+b+c=0

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  12. If a^(1/3)+b^(1/3)+c^(1/3)=0 show that (a+b+c)^(3)=27 abc

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  13. If x^(a)=y^(b)=(xy)^(c ) prove that ab=c(a+b)

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  14. If x^(a)=c^(b) and x^(c )=c^(a) show that a^(2)=bc

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  15. If x^(y)=y^(x) show that (x/y)^(x/y)=x^((x)/(y)-1) if further x=2y t...

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  16. If p^(a)=q^(b)=r^(c ) and pqr=1 show that ab+bc+ca=0

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  17. If 2^(x)=3^(y)=12^(z) show that xy=z(x+2y)

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  18. If (a-(1)/(a))^(2)=3 show that a^(6)+(1)/(a^(6))=110

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  19. If x^(3)=y^(4) prove that (x/y)^(4/3)+(y/x)^(3/4)=x^(1/3)+y^(-1/4)

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  20. If a^(x)=b,b^(y)=c,c^(z)=a show that xyz =1 (a,b,c positive num...

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