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The cube of a number or any other mathematical expression is denoted by a superscript 3, for example 23 = 8 or (x + 1)3 . The cube is also the number multiplied by its square : n3 = n × n2 = n × n × n. The cube function is the function x ↦ x3 (often denoted y = x3) that maps a number to its cube. It is an odd function, as.
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".
Power of 10. Visualisation of powers of 10 from one to 1 trillion. A power of 10 is any of the integer powers of the number ten; in other words, ten multiplied by itself a certain number of times (when the power is a positive integer). By definition, the number one is a power (the zeroth power) of ten. The first few non-negative powers of ten are:
The Third Crusade (1189–1192) was an attempt led by three European monarchs of Western Christianity ( Philip II of France, Richard I of England and Frederick I, Holy Roman Emperor) to reconquer the Holy Land following the capture of Jerusalem by the Ayyubid sultan Saladin in 1187. For this reason, the Third Crusade is also known as the Kings ...
A country's gross domestic product (GDP) at purchasing power parity (PPP) per capita is the PPP value of all final goods and services produced within an economy in a given year, divided by the average (or mid-year) population for the same year. This is similar to nominal GDP per capita but adjusted for the cost of living in each country.
History of Europe. The history of Europe is traditionally divided into four time periods: prehistoric Europe (prior to about 800 BC), classical antiquity (800 BC to AD 500), the Middle Ages (AD 500–1500), and the modern era (since AD 1500). The first early European modern humans appear in the fossil record about 48,000 years ago, during the ...
Cube root. In mathematics, a cube root of a number x is a number y such that y3 = x. All nonzero real numbers have exactly one real cube root and a pair of complex conjugate cube roots, and all nonzero complex numbers have three distinct complex cube roots. For example, the real cube root of 8, denoted , is 2, because 23 = 8, while the other ...
The divided power envelope is a fundamental tool in the theory of PD differential operators and crystalline cohomology, where it is used to overcome technical difficulties which arise in positive characteristic . The divided power functor is used in the construction of co-Schur functors.