Math 10 Week # 3

Following the conclusion to our numbers unit,  we started learning more about exponents, powers, and how we deal with them. There are many different ways we can use exponents as well as many different types of them like negative and fraction exponents. Today, I am going to show you how to use integral exponents. These are numbers with exponents that are negative and because of that, we need to change them into a positive to make it easier to solve the expression.

For our first example, we are going to solve . First, we have many ways we can go about this. In these expressions, we can start with the multiplication law, division law, power of a power law, or the negative exponent law. It’s all about your preference. For me, I am going to begin with the power of the power law because it makes it easier for me to get rid of the brackets. So to do this, we multiply the exponent outside the brackets with the exponents on the inside. We multiply all exponents in the brackets so x gains a -2 as an exponent (because we multiply -2 by the numbers exponent which is 1) and -7 exponent is also -2 for the same reason. Next, I am going to use the negative exponent law to get rid of negative exponents to make it easier to read. In this case, we are going to pretend that negative exponents are unhappy. So as we see that at the top, the and are both unhappy numbers, so because of this, we are going to bring them down to the denominator. As for the bottom of the fraction, is also unhappy so we are going to move it to the numerator. By doing this, all exponents are now happy. After, I like to use the multiplication law and multiplying numbers with the same base together. When doing this, exponents don’t listen to what they are told to do so instead of exponents multiplying with each other, exponents are added together.On the bottom we can multiply -7 with to make . Once this is done, i like to simplify any numbers with exponents possible so we turn into -343. And finally, we are going to finish off with the division law. Similar to the multiplication law, instead of exponents dividing into each other, they don’t like to listen and instead subtract from each other. The last thing we are going to do is divide with its equivalent on the bottom, it instead subtracts with each other creating zero. However, we arent done because we have a number on the denominator but not in the numerator. In math, we are not allowed to have no number on the numerator so we add a 1 and our final answer is .