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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. The word "raised" is usually omitted, and sometimes "power" as well, so 3 5 can be simply read "3 to the 5th", or "3 to the 5".
Exponential functions with bases 2 and 1/2. In mathematics, the exponential function is the unique real function which maps zero to one and has a derivative equal to its value. . The exponential of a variable is denoted or , with the two notations used interchangeab
The limit, should it exist, is a positive real solution of the equation y = x y. Thus, x = y 1/y. The limit defining the infinite exponential of x does not exist when x > e 1/e because the maximum of y 1/y is e 1/e. The limit also fails to exist when 0 < x < e −e. This may be extended to complex numbers z with the definition:
In arithmetic and algebra, the fifth power or sursolid [1] of a number n is the result of multiplying five instances of n together: n 5 = n × n × n × n × n. Fifth powers are also formed by multiplying a number by its fourth power, or the square of a number by its cube. The sequence of fifth powers of integers is:
The first three values of the expression x[5]2. The value of 3[5]2 is 7 625 597 484 987; values for higher x, such as 4[5]2, which is about 2.361 × 10 8.072 × 10 153 are much too large to appear on the graph. In mathematics, pentation (or hyper-5) is the fifth hyperoperation.
In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial.According to the theorem, the power (+) expands into a polynomial with terms of the form , where the exponents and are nonnegative integers satisfying + = and the coefficient of each term is a specific positive integer ...
In a thread on X, formerly known as Twitter, Murrill said "H.B. 71 requires Louisiana classrooms to reflect certain displays of the Ten Commandments as students return from winter break. This week ...
In scientific notation, this is written 9.109 383 56 × 10 −31 kg. The Earth's mass is about 5 972 400 000 000 000 000 000 000 kg. [21] In scientific notation, this is written 5.9724 × 10 24 kg. The Earth's circumference is approximately 40 000 000 m. [22] In scientific notation, this is 4 × 10 7 m. In engineering notation, this is written ...