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Find the value of [[a/b]^(sqrt(99)-sqrt(...

Find the value of `[[a/b]^(sqrt(99)-sqrt(97))]^(sqrt(99)+sqrt(97))`

A

`b^(2)/a^(2)`

B

`sqrt(b/a)`

C

`sqrt(b/a)`

D

`a^(2)/b^(2)`

Text Solution

Verified by Experts

The correct Answer is:
D
Apply laws of exponents.
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PEARSON IIT JEE FOUNDATION-INDICES-CONCEPT APPLICATION LEVEL 2
  1. Find the value of [[a/b]^(sqrt(99)-sqrt(97))]^(sqrt(99)+sqrt(97))

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  2. If 1/((243)^(x))=(729)^(y)=3^(3), then find the value of 5x+6y.

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  3. ((1/x+y)^((a+b))(1/y-x)^(-(p+q)))/((1/x-y)^(-(p+q))(x+1/y)^((a+b)))=

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  4. If 7^((5x-8))xx5^((x+2))=30625, then find x, an integer.

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  5. If a^x = b^y = a^z and a^3 = b^2 c, then 3/x - 2/y =

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  6. Simplified form of ((p+1/q)^((p-q))(p-1/q)^((p+q)))/((q+1/p)^((p-q))(...

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  7. If X = a^1 b^2 c^3 ... z^26 and Y = z^1 y^2 x^3... a^26 where, abcd...

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  8. If a^(b)=256, then find the maximum possible value of a.b, where a and...

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  9. If 11^x = 3^y = 99^z, then 1/x + 1/y + 1/z

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  10. If a^(b^t) = 6561, then find the least possible value of (a.b.c), wh...

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  11. If (xy)^((a - 1)) = z, (yz)^((b - 1)) = x and (xz)^((c-1)) = y, and ...

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  12. If x^(200) lt 3^(300), then the greatest possible integral value of x.

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  13. If 5^(n-3)=625, then 5^(n+3) is .

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  14. Find the value of (0.00243)^(3/5)+(0.0256)^(3/4).

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  15. [((a^(0)+b^(0))(a^(0)-b^(0)))/(a^(2)-b^(2))]^(0^(+^(5)))" "("where "...

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  16. If (1331)^(-x)=(225)^(y) where x and y are integers, then find the val...

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  17. If (sqrt(3))^(x+y)=9 and (sqrt(2))^(x-y)=32, then 2x+y is .

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  18. If 6^(x-y)=36 and 3^(x+y)=729, then find x^(2)-y^(2).

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  19. If p^(q')=512 find the minimum possible value of (p) (q) (r), where p,...

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  20. If 2^(x+y)=128 and 4^(x-y)=16, then find x/y.

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