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Prove that: 1/(1+x^(b-a)+\ x^(c-a))+1/(1...

Prove that: `1/(1+x^(b-a)+\ x^(c-a))+1/(1+x^(a-b)+\ x^(c-b))+1/(1+x^(b-c)+x^(a-c))=1`

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If y=1/(1+x^(a-b)+x^(c-b))+1/(1+x^(b-c)+x^(a-c))+1/(1+x^(b-a)+x^(c-a)), then (dy)/(dx) is equal to (a) 1 (b) (a+b+c)^(x+b+c-1) 0 (d) none of these

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Assuming that x is a positive real number and a ,\ b ,\ c are rational numbers, show that: ((x^a)/(x^b))^(1/(a b))\ ((x^b)/(x^c))^(1/(b c))\ \ ((x^c)/(x^a))^(1/(a c))=1

Prove that: ((x^a)/(x^(b)))^(a^(2+a b+b^2))\ xx\ ((x^b)/(x^(c)))^(b^(2+b c+c^2))\ xx\ ((x^c)/(x^(a)))^(c^(2+c a+a^2))=1

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ICSE-INDICES [EXPONENTS]-EXERCISE 7 (C)
  1. Prove that: 1/(1+x^(b-a)+\ x^(c-a))+1/(1+x^(a-b)+\ x^(c-b))+1/(1+x^(b-...

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  2. Evaluate : 9^((5)/(2)) - 3xx8^(0)-((1)/(81))^(-(1)/(2))

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  3. Evaluate : (64)^((2)/(3))-root(3)(125)-(1)/(2^(-5))+(27)^(-(2)/(3))...

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  4. Evaluate : [(-(2)/(3))^(-2)]^(3)xx((1)/(3))^(-4)xx3^(-1)xx(1)/(6)

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  5. Simplify : (3xx9^(n+1)-9xx3^(2n))/(3xx3^(2n+3)-9^(n+1))

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  6. Solve : 3^(x-1)xx5^(2y-3)=225.

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  7. If ((a^(-1)b^(2))/(a^(2)b^(-4)))div((a^(3)b^(-5))/(a^(-2)b^(3)))=a^(x)...

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  8. If 3^(x +1) = 9^(x - 3), find the value of 2^(1 + x).

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  9. If 2^(x)=4^(y)=8^(z) and (1)/(2x)+(1)/(4y)+(1)/(8z)=4 find the value o...

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  10. If (9^n\ x\ 3^2\ x\ 3^n-\ 27^n)/(3^(3m)\ x\ 2^3)=1/(27) , prove that m...

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  11. Solve for x : x:(13)^sqrt(x)=4^(4)-3^(4)-6.

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  12. If 3^(4x)=(81)^(-1)and(10)^((1)/(y))=0.0001, value of 2^(-x) xx 16^(y)...

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  13. Solve the equation: 3(2^x+1)-2^(x+2)+5=0

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  14. If (a^(m))^(n)=a^(m).a^(n), find the value of : m(n - 1) - (n - 1)

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  15. If m = root(3)(15) and n = root(3)(14), find the value of m - n - (1)/...

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  16. Evaluate : (2^(n)xx6^(m+1)xx10^(m-n)xx15^(m+n-2))/(4^(m)xx3^(2m+n)xx25...

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  17. Evaluate : ((x^(q))/(x^(r )))^((1)/(qr))xx((x^(r ))/(x^(p)))^((1)/(rp)...

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  18. Prove that: (a^(-1))/(a^(-1)+b^(-1))+(a^(-1))/(a^(-1)-b^(-1))=(2b^2)/(...

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  19. Prove that: (a+b+c)/(a^(-1)\ b^(-1)+b^(-1)\ c^(-1)+c^(-1)a^(-1))=a b c

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  20. Evaluate : (4)/((216)^(-2//3))+(1)/((256)^(-3//4))+(2)/((343)^(-1//3)...

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