Which of the following statistics is defined as the 50th percentile?

a. the mean
b. the median
c. the mode
d. the interquartile range
e. the standard deviation

9514 1404 393

Step-by-step explanation:

The applicable rules of exponents are ...

  (a^b)(a^c) = a^(b+c)

  (a^b)^c = a^(bc)

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The left-side expressions (all the same) can be simplified to ...

  (7^(1/5))·(49^(7/5)) = (7^(1/5))·((7^2)^(7/5))

  = (7^(1/5))·(7^(14/5)) . . . . . . matches 3rd right-side expression

  = 7^(1/5 +14/5) = 7^(15/5) = 7^3

  = 343 . . . . . . . . . . . . . . . . . . matches 1st right-side expression

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49 is obviously not equivalent to 343.

49^(2/10) is obviously not equivalent to 49^(7/5).