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If (9^n*3^2*(3^(-n/2))^(-2)-(27)^n)/(3^...

If `(9^n*3^2*(3^(-n/2))^(-2)-(27)^n)/(3^(3m)*2^3)=1/(27),` Prove that `m-n=1.`

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RD SHARMA ENGLISH-EXPONENTS OF REAL NUMBER-All Questions
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  2. Show that : (i) x^(a(b-c))/(x^(b(a-c)))/((x^b)/(x^a))^c=1, (ii)((x^...

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  3. If (9^n*3^2*(3^(-n/2))^(-2)-(27)^n)/(3^(3m)*2^3)=1/(27), Prove that ...

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  4. If 27^x=9/(3^x), find xdot

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  5. Find the values of x in each of the following : (i)2^(5x)-:2^x=2^(20)...

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  6. Evaluate each of the following: (i)5^2*5^4 (ii) 5^8+5^3 (iii) (3...

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  7. Evaluate each of the following: (i)(2/(11))^4*((11)/3)^2*(3/2)^3 (i...

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  9. Assuming that x , y are positive real numbers, simplify each of the fo...

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  10. Simplify : ((25)^(3/2)*(243)^(3/5))/((16)^(5/4)*(8)^(4/3))

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  11. Simplify: ((81)/(16))^(-3/4)*[((25)/9)^(-3/2)-:(5/2)^(-3)]

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  12. If x , y ,z are positive real numbers show that: sqrt(x^(-1)y)dotsqrt(...

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  13. Evaluate each of the following (i) 5^2 x 5^4 (ii) 5^8 divide 5^3 (i...

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  14. Evaluate each of the following (i) (2/11)^4 x (11/3)^2 x (3/2)^3 (ii...

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  15. If a=2 and b=3 then find the values of each of the following (i) a^a...

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  16. Evaluate each of the following removing radical sign and negative indi...

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  17. Evaluate each of the following (i) 5^2\xx\ 5^4 (ii) (3^2)^3

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  18. Evaluate each of the following (i)((11)/(12))^3 (ii) (3/4)^(-3)

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  19. Evaluate each of the following: (i)\ (2/(11))^4\ xx\ \ ((11)/3)^2\ xx...

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