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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^b)/(x^c))^a\ ((x^c)/(x^a))^b\ ((x^a)/(x^b))^c=1`

A

`x^(abc)`

B

`1`

C

`x^(ab+bc+ca)`

D

`x^(a+b+c)`

Text Solution

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The correct Answer is:
B
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MTG IIT JEE FOUNDATION-EXPONENTS AND POWERS-EXERCISE (MULTIPLE CHOICE QUESTION) (LEVEL -I)
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  2. (4^(5)xx3^5)/((12)^(5) xx9^2)=?

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

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  4. Differentiate ((x^(a))/(x^(b)))^(a+b)*((x^(b))/(x^(c)))^(b+c)*((x^(c))...

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  5. The value of (8^(-25)-8^(-26)) is 7xx8^(-25) b. 7xx8^(-26) c. 8xx8^(-...

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  6. 49xx49xx49xx49=7^? 4 b. 7 c. 8 d. 16

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  7. Number of prime factors is (6^(12)xx(35)^(28)xx(15)^(16))/((14)^(14)xx...

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  8. If 5^((x+3))=25^((3x-4)), then the value of x is 5/(11) b. (11)/5 c. (...

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  9. If 2^(n-1)+2^(n+1)=3, then n is equal to 0 b. 2 c. -2 d. -1

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  10. If 3^(x)-3^(x-1)=18, then the value of x^x is

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  11. By what number should ((2)/(3))^3 be divided so that the quotient is (...

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  12. By what number should ((3)/(5))^2 be multiplied so that the product i...

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  13. Find the value of x so that 5^(2x)xx5^(3)=5^6.

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  14. Find the value of x, if (2^(x-1)*4^(2x+1))/(8^(x-1))=64.

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  15. If 800xx(x^3)^(2)=8xx10^8, then x=

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  16. Express 32xx10000000 in standard form.

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  17. Usual form of -4.8xx10^8 is

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  18. Simplify : 7^(16)xx7^(5)xx((1)/(7))^(11)

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  19. If [5^(9)xx5^(3)]div[5^(15)div5^(3)]=5^m, then find the value of m.

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  20. If (x)/(y)=((2)/(3))^(3)div((3)/(2))^2, then the value of ((x)/(y))^3 ...

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