Exponentiation is a mathematical operation, written a^n, involving two numbers, the base a and the exponent n. When n is a positive integer, exponentiation corresponds to repeated multiplication:
just as multiplication by a whole number corresponds to repeated addition:
The exponent is usually shown as a superscript to the right of the base. The exponentiation a^n can be read as: a raised to the n-th power or a raised to the power [of] n, or more briefly: a to the n-th power or a to the power [of] n, or even more briefly: a to the n. Some exponents can be read in a certain way; for example a^2 is usually read as a squared and a^3 as a cubed.
The power a^n can also be defined when the exponent n is a negative integer. When the base a is a positive real number, exponentiation is defined for real and even complex exponents n. The special exponential function e^x is fundamental for this definition. It enables the functions of trigonometry to be expressed by exponentiation. However, when the base a is not a positive real number and the exponent n is not an integer, then an cannot be defined as a unique continuous function of a.
Exponentiation where the exponent is a matrix is used for solving systems of linear differential equations.
just as multiplication by a whole number corresponds to repeated addition:
The exponent is usually shown as a superscript to the right of the base. The exponentiation a^n can be read as: a raised to the n-th power or a raised to the power [of] n, or more briefly: a to the n-th power or a to the power [of] n, or even more briefly: a to the n. Some exponents can be read in a certain way; for example a^2 is usually read as a squared and a^3 as a cubed.
The power a^n can also be defined when the exponent n is a negative integer. When the base a is a positive real number, exponentiation is defined for real and even complex exponents n. The special exponential function e^x is fundamental for this definition. It enables the functions of trigonometry to be expressed by exponentiation. However, when the base a is not a positive real number and the exponent n is not an integer, then an cannot be defined as a unique continuous function of a.
Exponentiation where the exponent is a matrix is used for solving systems of linear differential equations.
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