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If (2/3)^x\ \ (3/2)^(2x)=(81)/(16), . th...

If `(2/3)^x\ \ (3/2)^(2x)=(81)/(16),` . then `x=` 2 (b) 3 (c) 4 (d) 1

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To solve the equation \((\frac{2}{3})^x \cdot (\frac{3}{2})^{2x} = \frac{81}{16}\), we can follow these steps: ### Step 1: Rewrite the equation We start with the equation: \[ \left(\frac{2}{3}\right)^x \cdot \left(\frac{3}{2}\right)^{2x} = \frac{81}{16} \] ...
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RD SHARMA-EXPONENTS OF REAL NUMBER-All Questions
  1. Which one of the following is not equal to ((100)/9)^(-3/2) ? (a)\ (9/...

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  2. When simplified (256)^-(4^((-3//2)\ )) is 8 (b) 1/8 (c) 2 (d) 1...

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  3. (5^(n+2) −6 xx 5^(n+1))/(3 xx 5^n − 2xx 5^(n+1)) is equal to ...

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  4. If a ,\ b ,\ c are positive real numbers, then sqrt(a^(-1)b)\ xx\ sqrt...

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  5. If (3^(2x-8))/(225)=(5^3)/(5^x) , then x= 2 (b) 3 (c) 5 (d) 4

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  6. If (2/3)^x\ \ (3/2)^(2x)=(81)/(16), . then x= 2 (b) 3 (c) 4 (d)...

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  7. If a ,\ b ,\ c are positive real numbers, then root(5)(3125\ a^(10)b^5...

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  8. The value of 64^(-1/3)\ (64^(1/3)-64^(2/3)), is 1 (b) 1/3 (c) -...

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  9. If sqrt(5^n)=125 , then 5^(nsqrt64 )= 25 (b) 1/(125) (c) 625 (d)...

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  10. If (16)^(2x+3)=(64)^(x+3), then 4^(2x-2)=64(b) 256 (c) 32 (d) 512

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  11. If a ,\ m ,\ n are positive integers, then {root(m)(sqrt a)}^(m n) is ...

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  12. If 2^(-m)\ xx1/(2^m)=1/4, then 1/(14)\ {(4^m)^(1//2)+\ (1/(5^m))^(-1)}...

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  13. If x=2\ \ and y=4, then (x/y)^(x-y)+\ (y/x)^(y-x)=

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  14. The value of m for which [{(1/(7^2))^(-2)}^(-1/3)]^(1/4)=7^m ,

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  15. If (2^(m+n))/(2^(m-n))=16 and a=2^(1/10) then ((a^(2m+n-p))^2)/((a^(m-...

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  16. The value of {(23+2^2)^(2/3)+\ (140-19)^(1/2)}^2 , is 196 (b) 289 (c...

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  17. If\ \ sqrt(2^n)=1024 ,\ \ then 3^(2(n/4-4))= 3 (b) 9 (c) 27 (d) ...

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  18. If (3^(5x)\ xx\ 81^2\ xx\ \ 6561)/(3^(2x))=3^7, then x= (a)\ 3 (b) ...

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  19. State the quotient law of exponents

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  20. The value of "{"8^(-4/3)-:2^(-2)")"^(1/2) is (a)1/2 (b) 2 (c) 1/4 (d...

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