a quicker /easier for computer persons is this 2^18 - 2^10 * 1^8 = 1024 ( 1K ) * 256 or you could do this 2^20 / 2^2 = 1M /4 - that removes the last x steps. In computer science 1K is well known and 1M is 1024^2 - I assume some have that memorized as well. I would have to work it out. but I think faster/easier than the steps provide. and I never thought of the 'if 1 is in the exponential chain' - that was way cool, but once you know that - forget doing the math above 1 - just drop it 1 and above - easy to explain - 1 on exp gives same - so all exp above are meaningless - just drop. that saves steps also.
I'm sorry. But at the time of 1:23 you make a mistake, bicause the X parameter is the product of power exponents 5 and 9, and here you are exponentiating powers, so the exponents must be multiplied together. Your question is... sqrt(((((2^6)^2)^1)^5)^9) so the exponents are 1/2, 6,2,1,5 and 9 Well, you can get the result by multiplying them together like 1/2*6*2*1*5*9=270 So the result is 2^270 ... ~1,89713759*10^81 By way of comparison... the average distance between the sun and the earth is 15.78*10^6 km and much, much smaller!
That's not how it's solved. The last two exponents are bracketed out and solved first, like this: sqrt(2^6^2^1^(5^9)). After solving (5^9), you have sqrt(2^6^2^1^953,125). Bracket out the last two powers, sqrt(2^6^2^(1^953,125)). 1^953,125 = 1, resulting in sqrt(2^6^2^1). Bracket out the last two powers: sqrt(2^6(2^1)). 2^1 = 2, so sqrt(2^6^2). Bracket out the last two powers: sqrt(2^(6^2)). This leaves sqrt(2^36). The square root of 2^36 is 2^18 which equals 262,144. QED.
Why not multiply all the exponents? And then solve it by dividing the full exponent by 2. If it is the root of 2. There is also a bug handling power 1. You will see it, if you set brackets around the term.
