In order to put other skills we learned this week to use (combining exponent laws) we need to know how to fully deal with the components within them, so I’m going to be explaining how to deal with integral exponents. Within expressions and equation’s you will need to know how to translate and transform negative exponents to simplify the equations/expressions further. Down below I showed how transforming the negative integers allows for simplifying the equation better.

Throughout this week we learned lessons, that built onto the new skills we learned the week before. I thought this one tied into my last weeks post of prime factorization well, because square roots remind me of simplifying of numbers, like used in prime factorization, you break the numbers down to help you solve the equation. One common problem with this process that can cause some confusion is that every mixed radical can be converted into an entire radical, while only some entire radicals can be expressed as a mixed number (depending if they have a factor that is a perfect square). There is an example of how you can convert these mixed radicals into entire ones.

In this first week we learned a few new lessons, but with these lessons the one that I think would be the most important is finding the prime factors of a number (as you need it to find the LCM (lowest common multiple) and the GCF (greatest common factor)). To find the prime numbers of a specific number you can use two different methods, the division table or the tree diagram. Every composite number can be expressed as a product of prime factors, for example 12 has these prime numbers 2,3 (a prime number is a whole number with only two factors 1, and itself). To find the prime factors I normally make a factor tree so I’m going to show you how to narrow down numbers to get to the prime factors. First you break it down into two using two whole numbers that multiply together to produce that number then you break down those new branches, and so on and so on.

The first step in solving this 3 operation equation is to multiply (1/2 x 3/6) which produces 3/12, so the new equation as shown on the next like is 1/2 + 3/12 – 2/6 in order to do our last two operations (addition and subtraction) we need to have the same denominators with all the fractions so we will 12 since 2 and 6 both can fit into 12. 1/2 * 6 and 3/6 * 2 we will get 6/12 + 3/12 – 4/12= we will simply just do addition and subtraction from left to right which will give us 5/12