Raise an exponent to an additional power

The tabloids have made small hay over the teaching advert in which the wrong answer to a mathematics question is shown on screen. The creators state that they knew this was wrong and the teacher in question was demonstrating a purposefully incorrect method of solving. The correct method was then shown, but for this advert was snipped out.

So yeah not very good editing, but it got me thinking - how many of the journalists would have spotted this, and how many would know what the answer is and why? If you were searching for an answer how would you even pose the question?

The question posed was (g²)⁷ or g to the power of 2 to the power of 7. Let's demonstrate a universal proof using standard terminology: (xⁿ)^m

Firstly let's examine xⁿ. As hopefully you are aware that means multiply x by itself n times. If n equalled 5 it could be written out in full as:

x∙x∙x∙x∙x (with ∙ meaning multiply)

So what happens when we 'add' another power to that? Well the same thing, we just multiply that by itself m times. Keeping n as 5 if we made m equal 6 we could write that out in full in the following format:

x∙x∙x∙x∙x∙
x∙x∙x∙x∙x∙
x∙x∙x∙x∙x∙
x∙x∙x∙x∙x∙
x∙x∙x∙x∙x∙
x∙x∙x∙x∙x

What we see here is x multiplied by itself a large number of times - how many times? Well from our formatting we can see that we will always have n columns and we'll always have m rows and our basic knowledge of algebra tells us that means we have n∙m x's which need to multiplied. Using our already established terminology on how to write that out results in x^n∙m or x multiplied by itself (n times m) times

Thus  (xⁿ)^m = x^n∙m

Returning to the original question is should be now clear that (g²)⁷ is the same as g^2∙7 or g¹⁴

Given my proof here it should also be obvious as to why it was squeezed out of a 30-second 'commercial'.