Algebra

by Boundless

exponent, and 243 is the power or, more specifically, the fifth power of 3, 3 raised to the fifth power, or 3 to the power of 5. The word "raised" is usually omitted, and very often "power" as well, so 3 5 is typically pronounced "three to the fifth" or "three to the five." Integer Exponents The exponentiation operation with integer exponents

n ⋅b From the associativity of multiplication, it follows that for any positive integers m and n b m+n = b m⋅b n Arbitrary Integer Exponents For non-zero b and positive n, the recurrence relation from the previous subsection can be rewritten as b n = b n+1 b By defining this

The following observations may be made: • Any number raised by the exponent 1 is the number itself. • Any nonzero number raised by the exponent 0 is 1; one interpretation of these powers is as empty products. • These equations do not decide the value of 0 0 . • Raising 0 by a negative exponent would imply division by 0, so it is left undefined. The identity b m+n = b m⋅b n initially defined only for positive

number. There is one nonzero digit to the left of the decimal point and the absolute value of the exponent on 10 records the number of places the original decimal point was moved to the left. If instead we have a very small number, such as 0.00059, we instead move the decimal place to the right, as in the following: 0.00059 = 5.9 10000 = 5.9 10 4 = 5.9⋅10 −4 15 In standard form, the number is written out as you are accustomed to, the ones digit to the farthest to the right (unless there is a decimal), then the tens digit to the left of the ones, and so on. In scientific notation, a number in standard notation with one nonzero digit to the left of the decimal is multiplied by ten to some power, as shown. Figure 1.8 Standard Form