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Assuming that x is a positive real numbe...

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

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To prove the equation \[ \left(\frac{x^a}{x^b}\right)^{a+b} \cdot \left(\frac{x^b}{x^c}\right)^{b+c} \cdot \left(\frac{x^c}{x^a}\right)^{c+a} = 1, \] we will follow these steps: ...
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RD SHARMA-EXPONENTS OF REAL NUMBER-All Questions
  1. Assuming that x is a positive real number and a ,\ b ,\ c are rational...

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  2. Assuming that x is a positive real number and a ,\ b ,\ c are rational...

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  3. Assuming that x is a positive real number and a ,b , c are rational nu...

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  4. If x is a positive real number and the exponents are rational number...

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  5. Show that: (i) (x^(a(b-c)))/(x^(b(a-c)))-:((x^b)/(x^a))^c=1, (ii) (...

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

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

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  9. If a ,\ b ,\ c are distinct positive prime integers such that a^2b^3c^...

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  10. Find the value of x , if 5^(x-3)\xx\ 3^(2x-8)=225

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  11. Solve the following equations: 2^(x-5)=256 (ii) 2^(x+3)=4^(x-1)

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  12. If 9^(x+2)=720+9^x , find the value of (4x)^(1/x)

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  13. Solve the equation for x: 2^(2x+1)=17. 2^x-2^3

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  14. Solve the equation for x 5^(2x+1)=6. 5^x-1

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  15. 3(a^4b^3)^10xx5(a^2b^2)^3

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  16. Simplify that: (2x^(-2)y^3)^3

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  17. Simplify that: ((4\xx\ 10^7)(6\ xx\ 10^(-5)))/(8\ xx\ 10^4)

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  18. Simplify that: (4a b^2\ (-5a b^3))/(10 a^2b^2)

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  19. Simplify that : ((x^2\ y^2)/(a^2b^3))^n

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  20. Simplify that: ((a^(2n-9))^6)/(a^(2n-4))

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