Inspired by Zandra Vinegar- part 2

Algebra Level 1

Let $n$ and $m$ be two distinct positive integers larger than 1, then which of these numbers is larger?

$\large n^{n^m} \text{ or } (n^n)^m$

{n^{n^m}}

{(n^n)}^ {m}

2 solutions

Zyberg Nee
Feb 13, 2016

Prior knowledge of problems with $x^{y^{z}}$ would make anyone answer immediately. However, if you had no such knowledge, you could take any numbers that satisfy $n$ and $m$ , for example: $n = 2$ and $m = 3$ and then try it out!

$2^{2^{3}}=2^{8}=\boxed{256}$

$(2^{2})^{3}=2^{6}=\boxed{64}$

$\boxed{256} > \boxed{64}$

n and m are less than 1

harish ghunawat - 5 years, 3 months ago

A Former Brilliant Member
Feb 14, 2016

$a^{b^c} > (a^b)^c$

That isn't true for all numbers

James D - 5 years, 3 months ago

$a^{b^{c}} > (a^b)^c$

$a^0=1; a \not = 0$

$2^{3^{4}} = 2^{81}$ > $(2^3)^4 = 8^4$ $2^{81} > 8^4$

A Former Brilliant Member - 5 years, 3 months ago

Inspired by Zandra Vinegar- part 2

2 solutions

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