Lana says there are #4^3# eggs in a dozen. Patrick says there are #3^4# eggs in a dozen. Is either person correct? Why?

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Answer 1 · 2017-10-09T01:39:09

No.
Here is why:
A dozen is 12.
#4^3 = 64 != 12#
#3^4 = 82 !=12#

Answer 2 · 2017-10-09T01:39:58

Neither of them are correct.

A dozen is #12#.

Let's evaluate each exponent to see if either are equal to #12#:

#4^3#

#=4\times 4\times 4#

#=64#

Since #64\ne 12#, Lana is incorrect.

#3^4#

#=3\times 3\times 3\times 3#

#=81#

Since #81\ne 12#, Patrick is also incorrect.

Therefore, neither Patrick nor Lana is correct.

Answer 3 · 2017-10-09T01:52:16

None of them are correct.

A dozen is defined as a group of 12 (twelve).

If we simplify each of the values, we get:

I will do it step by step to avoid confusion.

#4^3#

#=4xx4xx4#

#=16xx4#

#=64#

#3^4#

#=3xx3xx3xx3#

#=9xx3xx3#

#=27xx3#

#=81#

Therefore, neither Lana nor Patrick are correct.

In fact, no expression of a value by the power of #x# will equal to #12#.

Hope this helps :)