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DQ#1 Due Date: Day 2 [Main forum] Post a response to the following: Why is it important to simplify radical expressions before adding or subtracting? How is adding radical expressions similar to adding polynomial expressions? How is it different? Provide a radical expression for your classmates to simplify. Consider participating in the discussion by simplifying your classmates’ expressions. Detail what would have happened or if the expression was not simplified first. Why is it important to simplify radical expressions before adding or subtracting? You have to simplify radical expressions before adding or subtracting because you can only add or subtract expressions with the same value inside the radical sign. How is adding radical expressions similar to adding polynomial expressions? How is it different? It is similar to adding polynomials because in polynomials you can also only add or subtract terms if they are like terms (variables with the same powers). In radical expressions, you can also only add or subtract like terms (the same value inside the radical). One main difference is that in polynomials, like terms are determined by the variables and their powers, while in radical expressions, like terms are determined by the value inside the root. Provide a radical expression for your classmates to simplify. Consider participating in the discussion by simplifying your classmates' expressions. Detail what would have happened or if the expression was not simplified first. Here is an example for the classmates: sqrt(180) - sqrt(20) Factor the 180 and 20: sqrt(5*36) - sqrt(5*4) Simplify: 6 * sqrt(5) - 2 * sqrt(5) Subtract: 4 * sqrt(5) If you did not simplify this expression first, you would end up with the wrong answer. DQ#2 Due Date: Day 4 [Main forum] Post a response to the following: Review section 10.2 (p. 692) of your text. Describe two laws of exponents and provide an example illustrating each law. Explain how to simplify your expression. How do the laws work with rational exponents? Provide the class with a third expression to simplify that includes rational (fractional) exponents. Consider responding to classmates who have chosen laws different from the ones you selected. Ask clarifying questions of your classmates to make sure you understand the laws. Practice simplifying your classmates’ expressions. Multiplication of like bases. When you multiply two exponential terms with the same base, you add the exponent. The formula is m^a * m^b = m^(a+b). Example: 2^3 * 2^3 = 2^(3+3) = 2^6 = 64 Division of like bases. When you divide two terms with like bases, you subtract the exponents: m^a / m^b = m^(a-b). Example: 2^6 / 2^4 = 2^(6-4) = 2^2 = 4 How do the laws work with rational exponents? Provide a third expression to simplify that includes rational (fractional) exponents The above laws are unchanged for fractional exponents... you still add the exponents for products, and subtract them for quotients. Example of the multiplication law with fractional exponents: 3^(1/3) * 3^(2/3) solution for that example 3^(1/3) * 3^(2/3) = 3^1 = 3 DQ#3 Due Date: Day 4 [Main forum] • After solving a rational equation, why is it important to check your answer? How is this done? What happens if you are checking a solution for the rational expression and find that it makes one of the denominators in the expression equal to zero? You have to make sure you haven’t introduced any false solutions. These are solutions that make any of the denominators equal to 0. If they are equal to 0, then you have to discard that solution. DQ#4 Due Date: Day 4 [Main forum] Rearrange the following equation to solve for “x”: y = sqrt(x) / z Multiply by z: Sqrt(x) = yz Square: x = (yz)^2 Mathlab, please make sure these haven’t changed. Number 1: Prin = 30 Other = -30 Number 2: Not real Number 3: F(0) = 1 Number 4: |a+4| Number 5: -5x Number 6: 8 Number 7: 5 |a| Number 8: Number 9: (xy^3z) ^ 1/5 Number 10: Choice C: 1/16807 Number 11: 6.5 ^ 11/28 Number 12: 1 x^ 5/7 Number 13: Choice C: 1/x^4 Number 14: x^6 y^2 Number 15: Choice A Number 16: 15x^2 √3 Number 17: Number 18: Choice A Number 19: Number 20: Number 21: Number 22: 30 √5 Number 23: 5bc^2 √2b Number 24: √2 Number 25: Number 26: Choice B: 28throot(x^17) Number 27: Number 28: 9 √3 Number 29: 69 √5 Number 30: (1+12a) √3a Number 31: -24 + 10√6 Number 32: Number 33: 14 Number 34: Number 35: 2√21 7 Number 36: Number 37: Number 38: