Examples of exponentiation

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More important for what follows is the operation of stream exponentiation.
Addition, subtraction, multiplication, division, and exponentiation of arbitrary expressions were possible without restriction.
We use exponentiation of maps to denote iterated composition.
Another interesting open problem is to find other applications of the technique of replacing exponentiation by hashing.
From fast exponentiation to square matrices: an adventure in types.
A moment's consideration should be enough to see that a similar tree is induced by expanding any expression involving exponentiation and products.
The cost data required transformation (exponentiation) to produce lognormal distributions, which had the effect of shrinking the actual correlations toward zero.
In general, if we allow functional result type in a safe recursion then we can define exponentiation.
In the sequel we show that the two definitions of exponentiation are equal using type-theoretic arguments only.
A number of new operators have been added, as well as many new identities (including those on exponentiation and shuffle elimination).
This characterization is given by the equational calculus that otherwise axiomatizes all equalities between arithmetical terms built up with variables, 1, product and exponentiation.
The function dig its returns the decimal representation of a number and () denotes exponentiation.
Another application is exponentiation with fractions as exponents.
This problem can also be thought of as the problem of formal equality-testing of multi-variate expressions involving only multiplications and exponentiation.
Exponentiation lacks the property of associativity, which we used for rewriting nested additions and multiplications.
This continued exponentiation throughout the latter stages of the implosion is attributed to the finite load thickness.
Exponentiation is the only operation whose arguments are instantiated to two different types.
Additionally, we illustrate the use of the parametricity theorem by proving exponentiation as reverse application correct.
Arguably, it more clearly illustrates the concept of denning exponentiation via divide-and-conquer on an appropriate data type.

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