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Prompted by another question on this site is this notation clear and unambiguous

$$x^{y^z}$$

One answer there seems to imply the meaning is $$x^{(y^z)}$$

Mathcad seams to agree with this making $2^{3^2} = 2^9 = 512$

On the other hand my Casio calculator iterprets this as

$$(x^y)^z$$

Making $2^{3^2} = (2^3)^2 = 8^2 = 64$

My simple question is either of these interpretations correct or do I need to put the brackets in to clarify as I always would anyway.

Community
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Warren Hill
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1 Answers1

5

The first one is used in mathematics, because $(x^y)^z$ is more simply written $x^{yz}$. The same goes for at least some programming languages (Haskell comes to mind), for the same reason.

Harald Hanche-Olsen
  • 31,960