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Polynomials - Negative Exponents Objective: Simplify expressions with negative exponents using the properties of exponents. There are a few special exponent properties that deal with exponents that are not positive. The first is considered in the following example, which is worded out 2 different ways: Example 1. a3 a3 ...
Simplifying Negative Exponents and Variables Brief notes, examples, and Worksheet (& solutions)
Negative Exponents What do negative exponents mean? We already know that positive exponents are a way of expressing repeated multiplication. For example: There are a few different ways of thinking about negative exponents, but in general, negative exponents are the opposite of positive ones.
The final topic in this lesson is negative exponents. Our goal when working with negative exponents is to make them positive, since we have already covered exponent rules with positive integers. One way to understand how to change a negative exponent to a positive exponent is to think about canceling common factors within a fraction. For instance,
As we decrease the power of 2 from 4 to 3 to 2 to 1, we eventually have a power of 0 and then negative powers –1 to –2 to –3 to –4. In addition, note that as the negative powers get larger the actual number gets smaller and smaller. For example, the expression.
But what does a negative exponent really mean? Lets do the same calculation long-hand by dividing the factors of x4 by the factors of x6. So we see that x to the power −2 is the same as one divided by x to the power +2. Here is the negative power rule for exponents. You will also see negative powers applied to products and fractions.
Negative exponents often arise when simplify ing ratios of monomials. This law of exponents is sometimes called the ratio of powers law: $ = xa-b , as long as xis not 0. However, notice that it works only when the bases are the same. 4318 Examples: x6 6-7 --! 1 X 7=x =x or xl x 3 a ~ 1a Sa _ -2a 1 X5a-X -X Ofx2a 14. Simplify. a. 4x6!5x7 c ...
