mat 117 week 1 DQ's 4 different explanation
mat 117 week 1 DQ's 4 different explanation
CSU - Dominguez hills
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Date Created: 11/16/15
Week 1 DQ 1 – Due Day 2 Please post a 150 300 word response to the following discussion question by clicking on Reply. Explain three rules for exponents listed in the chart on p. 239 (section 4.2). Do not explain the first two definitions listed in the table (Exponent of 1 or 0). Create an expression for your classmates to solve that uses scientific notation and at least one of the rules for exponents you have described. Consider responding to our classmates by assisting them in solving the problem you created, developing their explanations of the rules of exponents, or describing reallife situations where their examples might exist. Explanation 1 The power rule The positive exponents are easy to solve as you just multiply the powers. (X with a power of 2)6 X26 = X 12 for a power if the problem has a negative exponent inside the parerethisis and a positive outside then the solution is positive and a fraction. 1 over X And the power number. if they are both negative then the power is positive. Raising a product to a power For any real number a and b and any integer n. (ab)power of n = a power of n b power of n to raise a product to the nth power, raise each factor toto the nth power Raising a quotient to a powerand any integer n for any real numbers a and b, b and o to raise a quotient to the nth power, raise both the numerator and the denominator to the nth power raising power to power (a power of 4)6 Explanation 2 The product rule involves multiplying a variable times itself to the exponent quanity stated and then multiplying by each answer of the exponent and then aquiring a condensed solution. If the bases are the same, then just add the exponents. Am*An*=Am+n The rule for raising a product to a power is distributing the variable to a corresponding exponent. (AB)n =An/Bn The power rule makes the integer or variable multiply by all exponents in the equation. There by making the solution to be Amn. (Am)n All the rules for exponents have much in common. Determining the proper multiplication steps to form a solution is the thing to keep in mind. The parentheses tell us where to apply the exponent. In earlier math the parenthesis also tell us to solve it first. The negatives and positives are similar in exponents as they are in regular equations. Example for Classmates: 22+ 23+4 3=? Explanation 3 The first rule is the Product Rule this is when you have a number raised to a power multiplied by another number raised to a power. The easiest way to get your solution is multiply the numbers and add the exponents. If you are dividing then you use the Quotient Rule. You divide the numbers and then subtract the exponents and in this specific rule the numbers that are being divided absolutely can not equal zero. The Power Rule is when a number is being raised to an exponent and the answer to that is being raised to another exponent. In this case you have your number and you multiply the two exponents together. There are several rules to exponents however they are fairly simple it seems. I will just remember the rules and I think this part of algebra will be fairly simple. Problems: 3 x 4 3 2 2 2 /3 4 2 (4 ) Explanation 4 Multiplying Powers with Like Bases So, for any number a and any positive integers m and n, a^m . a^n = a^m+n When multiplying with exponential notation, if the bases are the same, keep the base and add the exponents. Dividing Powers with Like Bases THE QUOTIENT RULE For any nonzero number a and any positive integers m and n, a^m/a^n = a^m-n. So, when dividing with exponential notation, if the bases are the same, keep the base and subtract the exponent of the denominator from the exponent of the numerator. Negative Integers as Exponents /E EXPONENT For any real number a that is nonzero and any integer n, a^-n = 1/a^n. Solve: a^5 . a^3 = Week 1 DQ 2 Please post a 150 300 word response to the following discussion question by clicking on Reply. How is dividing a polynomial by a binomial similar to or different from the long division you learned in elementary school? Can understanding how to do one kind of division help you with understanding the other kind? What are some examples from real life in which you might use polynomial division? Explanation 1 Polynomial division is quite similar to the method of long division that I was taught back in my elementary school. Instead of using numbers as we did back in elementary school, there are now variables to deal with. However, the process is effectively the same. We go through the problem term by term, step by step just like in numerical long division. The problems steps are the same and can result in remainders. If you understand how to do the numerical type of long division, it is quite easy to extend the knowledge to polynomial division. As long as you know how to multiply monomial terms with variables equivalent to multiplication of numbers in the long division process and subtraction of terms equivalent to the subtraction in numerical long division, the actual process is the same. Also addition can be used to check certain answers within the problem. A person can use polynomial division in real life if they are trying to build on to a room or garage if the length is known and the perimeter is needed Explanation 2 When dividing polynomials by a binomial it is actually very similar due to the fact the you are using the same steps as you would when you are dividing as such in long division, the differences that you would see are that you are using variables in your division instead of just numbers, but like I said earlier the steps are the same first you divide then multiply then subtract and finally bring down the next term. I think that it is very helpful to understand one kind of division that will help you when it is similar to another kind. This will help you better understand more on how to do the problems that are different just because you have an understanding or the steps that you need to do. To be honest I can not think of any examples that would be related to real life experiences right off the top of my head, I am sure there are many examples but I can not think of any right now. Explanation 3 Dividing by a Polynomial by a Binomial The long division as it is performed in arithmetic, we divide, and we repeat the following procedure. To carry out long division: 1. Divide, 2. Multiply, 3. Subtract, and 4. Bring down the next term. Then, we repeat the process two more times. We check by multiplying the quotient by the divisor, and adding the remainder. Looking at long division with polynomials, we use this procedure when the divisor is not a monomial; we write polynomials in descending order and then write in missing terms. This adding, subtracting, dividing, and multiplying are used in everyday scenarios, and are a very useful tool. When you learn one kind of division it does help in understanding the other. This type of dividing is useful in measuring rooms or spaces of area, I used it recently in adding an additional room on to a rental home I just purchased. Explanation 4 Dividing a polynomial by a binomial is similar to what was learned in elementary school, scary at first glance. In elementary school you did not have to divide multiple expressions at the same time. You would combine them and then divide. This way seems quicker for the type of problems that are being solved. Remembering to use the exponents and the way a remainder is written are the only differences I can see at this point. I think knowing how to divide one way also helps you to understand how to do it another way. It is the working with the exponents and the function signs that confuses me at times. You could use this type of division for figuring how much of something it would take to fill or cover a given area such as lawn seed, paint, roofing, or siding. Doing construction for most of my life I used it a lot and did not know that it had a term associated to it
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