Basic Combinations

Since 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 Ten

For 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 Relationship

The 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 Functions

The hyperbolic functions can be defined in terms of exponentials.

An applications of the hyperbolic tangent is in calculating the speed of ocean waves.

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