+2446 Okay, I will attempt to simplify the expression of \((p^{-6p^2})^{-3}\) with only positive exponents:
| \((p^{-6p^2})^{-3}\) | Use the exponent rule that \(a^{-b}=\frac{1}{a^b}\) |
| \(\frac{1}{(p^{-6p^2})^3}\) | Use the exponent rule that states that \((a{^b})^c=a^{b*c}\). |
| \(\frac{1}{p^{-6p^2*3}}\) | Combine like terms in the exponent. |
| \(\frac{1}{p^{-18p^2}}\) | This expression is simplified as much as possible. |
+2446 Unfortunately, writing out such an unthinkably vast number is impossible; there are approximately \(10^{80}\) atoms in the observable universe. Googolplex is \(10^{10^{100}}=10^{10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}\). Therefore, you could write a digit on every atom and still have not scratched the surface.
Even if we assume that there are an infinite amount of atoms, we still cannot write the number out. Assuming that a normal human being can write two digits every second, it would take \(1.51*10^{91}\) years to write. That is \(1.1*10^{81}\) times the expected life expectancy of the entire universe.
The conclusion you should be gathering here is that writing out this number on a piece of paper is unfeasible.
Writing it digitally is a different story, however. Assuming a typical book is a 400 pages long, a book can print \(10^6\), or a million, zeroes on it. This would require \(10^{94}\), or 10 trigintillion, volumes before the number is written in its entirety. Then, I found this website, http://www.googolplexwrittenout.com/, that does exactly that! Write the entire number from start to finish. You can even order one of the volumes! That's crazy!
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