What is the answer and how to solve these type of exponent questions which are in the form a^b^c^d

Edit:

The answer is 1, which is easy to calculate, what I want to understand is how do we generally solve exponent questions of the type: a^b^c^d.

Is the answer 1?

You can rewrite 4 as 2^2. So the numerator will be 2^32. The denominator is also 2^32 as 2^5 = 32. The answer should be 1.

My aim wasn’t to find the answer, but a method that can be applied to exponent questions like a^b^c^d.

Sorry, I guess my question misled you, I will edit it.

If an exponent is of the form a^b^c^d, start by calculating c^d first and then move downwards.

For example if there’s an exponent 1^2^2^2, calculate 2^2 first which will give you 4. Then our exponent reduces to 1^2^4. Then calculate 2^4 = 16. Now we have reduced this exponent to 1^16 = 1

But what if the number is big, like 32^16^16^8 ? Calculating wouldn’t be an option, right ? So how would you solve this one ?

They would never ask such question in gre

Thanks

Yes!!

Such questions will not be asked but if you still want to solve, you can start by converting those numbers into powers of 2 then using the identities of exponents to multiply or add the powers and then recursively move down the chain.

I know the method, but I am unable to get 2^32 rather I am getting 2^16 (The denominator and numerator both simplify to 2^32).

That is the reason I asked this doubt.