Basic CombinationsSince the raising of a number n to a power p may be defined as multiplying n times itself p times, it follows that The rule for raising a power to a power can also be deduced 
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Powers of TenFor very large or very small numbers, it convenient to use the "scientific notation", i.e., to express the numbers in terms of a power of 10. Standard prefixes are used to denote certain powers of 10: 
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Radical Combinations 
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Euler RelationshipThe trigonometric functions are related to a complex exponential by the Euler relationship From these relationships the trig functions can be expressed in terms of the complex exponential: 
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Hyperbolic FunctionsThe hyperbolic functions can be defined in terms of exponentials. There are closedform expressions for the inverse hyperbolic functions: An application of the hyperbolic tangent is in calculating the speed of ocean waves. The hyperbolic cosine and its inverse are encountered in fluid friction in the case of quadratic drag. 
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