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When an exponent is a positive integer, that exponent indicates how many copies of the base are multiplied together. For example, 3 5 = 3 · 3 · 3 · 3 · 3 = 243. The base 3 appears 5 times in the multiplication, because the exponent is 5. Here, 243 is the 5th power of 3, or 3 raised to the 5th power.
When exponents were introduced in the 16th and 17th centuries, they were given precedence over both addition and multiplication and placed as a superscript to the right of their base. [2] Thus 3 + 5 2 = 28 and 3 × 5 2 = 75. These conventions exist to avoid notational ambiguity while allowing notation to remain brief. [4]
In arithmetic and algebra, the seventh power of a number n is the result of multiplying seven instances of n together. So: n 7 = n × n × n × n × n × n × n.. Seventh powers are also formed by multiplying a number by its sixth power, the square of a number by its fifth power, or the cube of a number by its fourth power.
When multiplication is repeated, the resulting operation is known as exponentiation. For instance, the product of three factors of two (2×2×2) is "two raised to the third power", and is denoted by 2 3, a two with a superscript three. In this example, the number two is the base, and three is the exponent. [26]
"A base is a natural number B whose powers (B multiplied by itself some number of times) are specially designated within a numerical system." [1]: 38 The term is not equivalent to radix, as it applies to all numerical notation systems (not just positional ones with a radix) and most systems of spoken numbers. [1]
Graphs of functions commonly used in the analysis of algorithms, showing the number of operations versus input size for each function. The following tables list the computational complexity of various algorithms for common mathematical operations.
Logarithms and exponentials with the same base cancel each other. This is true because logarithms and exponentials are inverse operations—much like the same way multiplication and division are inverse operations, and addition and subtraction are inverse operations.
In mathematics, a product is the result of multiplication, or an expression that identifies objects (numbers or variables) to be multiplied, called factors.For example, 21 is the product of 3 and 7 (the result of multiplication), and (+) is the product of and (+) (indicating that the two factors should be multiplied together).
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