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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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Show 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

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 find (dy)/(dx) at e^(a^(b^(c )))

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

Show that: (i)\ (x^(a-b))^(a+b)\ (x^(b-c))^(b+c)\ (x^(c-a))^(c+a)=1 (ii)\ {(x^(a-a^(-1)))^(1/(a-1))}^(a/(a+1))=x

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

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

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

Simplify: (i)\ ((x^(a+b))/(x^c))^(a-b)\ ((x^(b+c))/(x^a))^(b-c)\ ((x^(c+a))/(x^b))^(c-a) (ii)\ ((x^l)/(x^m))^(1/(lm))\ xx\ ((x^m)/(x^n))^(1/(mn))\ xx\ \ ((x^n)/(x^l))^(1/(ln))

Show that : (x^(a(b-c)))/(x^(b(a-c)))÷((x^b)/(x^a))^c=1 ((x^(a+b))^2(x^(b+c))^2 (x^(c+a))^2)/((x^a x^b x^c)^4)=1

RD SHARMA ENGLISH-EXPONENTS OF REAL NUMBER-All Questions
  1. Prove that: ((x^a)/(x^b))^c\xx\ ((x^b)/(x^c))^a\ xx\ ((x^c)/(x^a))^b=1

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

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

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

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  6. If a b c=1,\ show that 1/(1+a+b^(-1))+1/(1+b+c^(-1))+1/(1+c+a^(-1))=1

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  7. Simplify the following: (i)\ (3^n\ xx\ 9^(n+1))/(3^(n-1)\ xx\ 9^(n-1))...

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  8. Simplify the following: (i)\ (5^(n+3)-\ 6\ xx\ 5^(n+1))/(9\ xx\ 5^n-2^...

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  9. Solve the following equations for x\ : (i)\ 7^(2x+3)=1 (ii)\ 2^(x+1)...

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  10. Solve the following equations for x\ : (i)\ 4^(2x)=1/(32) (ii)\ 4^...

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  11. Solve the following equations for x\ : (i)\ 2^(2x)-\ 2^(x+3)+2^4=0 ...

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  12. If 49392=a^4b^2c^3, find the value of a ,\ b\ a n d\ c , where a ,\ b\...

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  13. If 1176=2^a xx\ 3^b xx\ 7^c , and a , b\ a n d\ c are natural numbers...

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  14. Given 4725=3^a5^b7^c , find the integral values of a ,\ b\ a n d\ c t...

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  15. If a=x y^(p-1),\ b=x y^(q-1) and c=x y^(r-1) , prove that a^(q-r)b^(r-...

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  16. Find the value of: (8/(27))^(1/3)

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  17. Find the value of : ((32)/(243))^(1/5)

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  18. Find the value of: (1/(64))^(1/6)

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  19. Evaluate each of the following by removing radical signs and negative ...

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  20. Evaluate each of the following by removing radical signs and negative ...

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