![]() Perform computations using numbers in scientific notation.Įxponents are used in many fields of science to write numbers in what is called scientific notation.Change a number from scientific notation to one without exponents.Write a given number in scientific notation.Identify a number that is in scientific notation.When working with negative exponents, be especially careful to use the laws of signed numbers properly. The laws of exponents will all apply to these new definitions. ![]() We can now write the third law of exponents simply as That means we cannot have a denominator equal to zero or a value of a variable that gives 0 0. ![]() We will agree from this point on in all the examples and problems that the variables must never take on values that will give a meaningless expression. It is understood here that x can take on any value except 0. These two seemingly different answers to the same problem lead to the following definition. We already know by dividing like factors that. If, then, this law is to apply in this special case, we must make the following definition. This will lead to two special cases, which in turn will require special definitions. We want to be able to use these laws for the integer zero and all the negative integers as well as the positive integers.įirst let us use only that part of law 3 that states that and make no requirements as to the relative size of a and b. If we pay special attention to law 3, we can see the reason for the definitions that follow. Now we will expand the concept of exponents to include all integers and not just the positive integers. Note that only the quantity inside the parentheses is raised to the indicated power. Here are some examples to refresh your memory. In chapter 7 we introduced and used the laws of exponents.
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