Do Bottom First Or Do Top First?

Algebra Level 1

All of the following numbers are equal to each other except for one. Which one?

2^{2^4}

2^{4^2}

4^{2^2}

1 solution

Armain Labeeb
Jul 31, 2016

Relevant wiki: Rules of Exponents

$\large \begin{aligned} 2^{ 4^{ 2 } } & =2^{ 16 } & & \\ 2^{ 2^{ 4 } } & =2^{ 16 } & & \\ 4^{ 2^{ 2 } } & =4^{ 4 } & =\left( 2^{ 2 } \right) ^{ 4 } & =2^{ 8 } \end{aligned}$

Thus $\boxed{4^{ 2^{ 2 } }}$ is not equal to the others.

Didnt understand, i'm too dumb :(

Gülhan Yilmaz - 4 years, 10 months ago

Tower of exponents rule. Click on wiki to redirect to a wiki where exponent rules are explained. You may find them helpful!

Armain Labeeb - 4 years, 10 months ago

I'm sorry but this is actually very hard to understand if you've not been taught on your wiki. It doesn't look like a "tower" - I assumed you were talking about (2^4)^2, for example, as this is how that representation is used in most of the books I read. To teach that one way of writing means one thing to everyone is actually quite misleading... With no context of what these sums were trying to evaluate, it took me a LONG time to realise you were talking about "towers".

The problem I have is that if you only learn of one approach, then you think this is standard. However, with no context, I would move to say that there are at least two answers to the above question with restrictions only occurring because of how you've been taught.

Llethraim . - 4 years, 8 months ago

Do Bottom First Or Do Top First?

1 solution

0 pending reports