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Simplify each of the following: (a)\ (7^...

Simplify each of the following: `(a)\ (7^n-3\ xx\ 7^(n+1))/(20\ xx\ 7^n-2\ xx\ 7^n)` ` (b)\ (5^n-6\ xx\ 5^(n+1))/(9\ xx\ 5^n-2^2xx\ 5^n)` `(c)\ (16\ xx\ 2^(n+1)-4\ xx\ 2^n)/(16\ xx\ 2^(n+2)-2\ xx\ 2^(n+2))`

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RD SHARMA ENGLISH-EXPONENTS OF REAL NUMBER-All Questions
  1. If a=2 and b=3 , then find the values of each of the following: (a)(...

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  2. Simplify the following (i) (3a^4b^3)(18 a^3b^5) (ii) (3a^7b^6)/(1...

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  3. Simplify each of the following: (a)\ (7^n-3\ xx\ 7^(n+1))/(20\ xx\ 7^n...

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  4. If (9^n\ xx\ 3^2\ xx\ (3^(-n/2))^(-2)-\ 27^n)/(3^(3m)\ xx\ 2^3)=1/(27)...

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

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

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

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

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

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

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

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  12. 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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  13. 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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  14. Prove that: (a^(-1))/(a^(-1)+b^(-1))+(a^(-1))/(a^(-1)-b^(-1))=(2b^2)/(...

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

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

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

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

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

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

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