Power of Numbers Power of Numbers The power of a number shows you how many times to use the number in a multiplication. It is written as a small number to the right and above the base number. The concept of logarithms arose from that of powers of numbers. If the properties of powers are familiar to you, you may quickly skim through the material below. If not--well, here are the details. Powers of a number are obtained by multiplying it by itself. For instance . 2.2 can be written 22 "Two squared" or "2 to the 2nd power" 2.2.2 = 23 ."Two cubed" or "2 to the 3rd power"" 2.2.2.2 = 24 "Two to the 4th power" or simply "2 to the 4th"" 2.2.2.2.2 = 25 "Two to the 5th power" or simply "2 to the 5th"" 2.2.2.2.2.2 = 26 "Two to the 6th power" or simply "2 to the 6th"" and so on... The number in the subscript is known as an "exponent." The special names for "squared" and "cubed" come because a square of side 2 has area 22 and a cube of side 2 has volume 23. Similarly, a square of side 16.3 has area (16.3)2 and a cube of side 9.25 has volume (9.25)3. Note the use of parentheses-they are not absolutely needed, but they help make clear what is raised to the second of 3rd power. Know More About :- Associated Property of Addition

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Multiplying powers :- Note that (23).(22) = 25 since the first term contributes three factors of 2 and the second term contributes two--together, 5 multiplications by 2. The same will hold is "2" is replaced by any number. So, if that number is represented by "x" we get (x3).(x2) = x5 and in general (since there is nothing special about 2 and 3 which will not hold for other whole numbers) (xa).(xb) = x(a+b) where a and b are any whole numbers. The most widely used powers by whole numbers, for users of the decimal system, are of course those of 10 101 = 10 ("ten") 102 = 100 ("hundred") 103 = 1000 ("thousand") 104 = 10,000 ("ten thousand") 105 = 100,000 ("a hundred thousand") 106 = 1,000,000 ("a million") Note that here the "power index" also gives the number of zeros. For larger numbers, it used to be that in the US 109 = 1,000,000,000 was called "a billion" while in Europe it was called a "milliard" and one had to advance to 1012 to reach a "billion." These days the US convention is gaining ground, but the world remains divided between nations where the comma denotes what we call "the decimal point", while the point divides large numbers, e.g. 109 = 1.000.000.000 (in the US commas would be used). It also should be noted that some cultures have assigned names to some other powers of 10--e.g. the Greeks used "myriad" for 10,000 while the Hebrew Bible named it "r'vavah," and in India "Lakh" still means 100,000. A 9-year old in 1920 coined the name "Googol" for 10100, but the word found little use beyond inspiring the name of a search engine on the world-wide web. Read More About :- Round Whole Numbers

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