# how to use barcode in c#.net Powers and Roots in Software Drawer Quick Response Code in Software Powers and Roots

116 Powers and Roots
Encoding Quick Response Code In None
Using Barcode drawer for Software Control to generate, create QR Code 2d barcode image in Software applications.
QR Code Decoder In None
Using Barcode recognizer for Software Control to read, scan read, scan image in Software applications.
15,6251/6 = 5 11/2 = 1 You can indicate that you want to use the negative value by placing minus signs like this: (161/4) = 2 (811/4) = 3 (15,6251/6) = 5 (11/2) = 1 Sometimes you will actually want to let either the positive or the negative value be used In cases of that sort, you should throw a plus-or-minus sign ( ) into the mix, like this: (161/4) = 2 (811/4) = 3 (15,6251/6) = 5 (11/2) = 1 Here s another possible confusion-maker Always pay special attention to where the parentheses are placed if you see a negative number raised to a power Also, be careful if there are no parentheses at all If there s any doubt, it s best to place extra parentheses in an expression so everyone knows exactly what it means For example, ( 2)3 = ( 2) ( 2) ( 2) = 8 and 23 = (23) = (2 2 2) = 8 In contrast to this, ( 2)4 = ( 2) ( 2) ( 2) ( 2) = 16 but 24 = (24) = (2 2 2 2) = 16
QR Code Generation In Visual C#
Using Barcode printer for Visual Studio .NET Control to generate, create QR-Code image in .NET framework applications.
Making QR Code In Visual Studio .NET
Using Barcode generator for ASP.NET Control to generate, create QR-Code image in ASP.NET applications.
Negative reciprocal powers We still have not explored what happens when we raise a number to a negative reciprocal-ofinteger power You can probably figure out the meaning of an expression such as 125 1/3, or
Generate QR In .NET
Using Barcode generation for VS .NET Control to generate, create Quick Response Code image in VS .NET applications.
Encode QR Code In VB.NET
Using Barcode generator for .NET framework Control to generate, create QR image in .NET applications.
Multiplying and Dividing with Exponents
Generate EAN-13 Supplement 5 In None
Using Barcode creation for Software Control to generate, create GS1 - 13 image in Software applications.
Generating UCC.EAN - 128 In None
Using Barcode creator for Software Control to generate, create UCC - 12 image in Software applications.
125 to the 1/3 power You take the 1/3 power of 125, which is 5, and then take the reciprocal of that, which is 1/5 Mathematically, it goes like this: 125 1/3 = 125 (1/3) = 1/(1251/3) = 1/5
Data Matrix Drawer In None
Using Barcode encoder for Software Control to generate, create ECC200 image in Software applications.
Make Code 128C In None
Using Barcode drawer for Software Control to generate, create Code 128 Code Set A image in Software applications.
Even roots of negative numbers What happens when you take an even root of a negative number The simplest example of this sort of problem is the square root of 1, but there are plenty of others What can you multiply by itself to get 1 Nothing that we ve defined yet! What is the 1/4 power of 16 Again, nothing we know of so far Mathematicians have defined quantities like this We will explore them in Chap 21 They re called imaginary numbers They have some fascinating properties Unlike division by 0 or the 0th root of 0, even roots of negative numbers can be tamed They are commonly used in science and engineering
Bar Code Printer In None
Using Barcode drawer for Software Control to generate, create bar code image in Software applications.
Make ANSI/AIM Code 39 In None
Using Barcode creation for Software Control to generate, create ANSI/AIM Code 39 image in Software applications.
Here s a challenge!
USPS PLANET Barcode Drawer In None
Using Barcode creator for Software Control to generate, create Planet image in Software applications.
Print UCC - 12 In None
Using Barcode generation for Office Excel Control to generate, create UCC - 12 image in Excel applications.
State the rule for negative reciprocal powers in general terms, where a is the base (the number to be raised to the power) and p is a positive integer
DataMatrix Generation In .NET Framework
Using Barcode printer for ASP.NET Control to generate, create DataMatrix image in ASP.NET applications.
Printing UCC-128 In VS .NET
Using Barcode printer for Visual Studio .NET Control to generate, create USS-128 image in VS .NET applications.
Solution
Make Data Matrix In None
Using Barcode generator for Online Control to generate, create ECC200 image in Online applications.
Recognize Bar Code In .NET Framework
Using Barcode decoder for VS .NET Control to read, scan read, scan image in VS .NET applications.
The power to which we want to raise the base is 1/p, where p is some positive integer (We know that 1/p will be negative, because a negative divided by a positive always gives us a negative) If we use the method from the above example where we evaluated 125 1/3, then we have a 1/p = a (1/p) = 1/(a1/p)
EAN / UCC - 14 Creation In Objective-C
Using Barcode printer for iPad Control to generate, create GTIN - 128 image in iPad applications.
Creating Data Matrix ECC200 In VB.NET
Using Barcode maker for VS .NET Control to generate, create ECC200 image in .NET framework applications.
Multiplying and Dividing with Exponents
When we have a certain base number raised to two different powers, we get two different quantities But the fact that those quantities have the same base lets us take shortcuts in multiplication and division
Multiply by adding Let s state the general case first, and then check out an example Imagine a number and call it a This can be any number except 0 It doesn t have to be an integer or even a rational number Now imagine the quantities a m and a n, where m and n are integers If you multiply these two quantities, you get the same result as if you add m to n, and then raise the base a to that power We can write this as an equation:
a ma n = a(m+n)