# 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?

Oct 9, 2017

No.
Here is why:
A dozen is 12.
${4}^{3} = 64 \ne 12$
${3}^{4} = 82 \ne 12$

Oct 9, 2017

Neither of them are correct.

#### Explanation:

A dozen is $12$.

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

${4}^{3}$

$= 4 \setminus \times 4 \setminus \times 4$

$= 64$

Since $64 \setminus \ne 12$, Lana is incorrect.

${3}^{4}$

$= 3 \setminus \times 3 \setminus \times 3 \setminus \times 3$

$= 81$

Since $81 \setminus \ne 12$, Patrick is also incorrect.

Therefore, neither Patrick nor Lana is correct.

Oct 9, 2017

None of them are correct.

#### Explanation:

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.

${4}^{3}$

$= 4 \times 4 \times 4$

$= 16 \times 4$

$= 64$

${3}^{4}$

$= 3 \times 3 \times 3 \times 3$

$= 9 \times 3 \times 3$

$= 27 \times 3$

$= 81$

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 :)