This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Here are the solutions to the problems. 4. Simplify: a) (cd-c^2)/((d-c)^2) Step 1: Factor out c from the numerator. (c(d-c))/((d-c)^2) Step 2: Cancel one (d-c) term from the numerator and denominator. (c)/(d-c) The simplified expression is (c)/(d-c). b) (2)/(3a) + (5)/(2b) Step 1: Find the least common multiple (LCM) of the denominators 3a and 2b, which is 6ab. Step 2: Rewrite each fraction with the common denominator. (2 · (2b))/(3a · (2b)) + (5 · (3a))/(2b · (3a)) (4b)/(6ab) + (15a)/(6ab) Step 3: Add the fractions. (4b+15a)/(6ab) The simplified expression is (4b+15a)/(6ab). c) (xcyz^2)/(abcxyz) Step 1: Identify common variables in the numerator and denominator. (x · c · y · z · z)/(a · b · c · x · y · z) Step 2: Cancel out the common variables (x, c, y, z). (z)/(ab) The simplified expression is (z)/(ab). 5. Write in standard form: Standard form (scientific notation) is written as a × 10^n, where 1 |a| < 10 and n is an integer. a) 368 Step 1: Move the decimal point to the left until there is one non-zero digit before the decimal point. 3.68 Step 2: Count the number of places the decimal point was moved. Since it was moved 2 places to the left, the exponent of 10 is 2. 3.68 × 10^2 The standard form is 3.68 × 10^2. b) 0.00006784 Step 1: Move the decimal point to the right until there is one non-zero digit before the decimal point. 6.784 Step 2: Count the number of places the decimal point was moved. Since it was moved 5 places to the right, the exponent of 10 is -5. 6.784 × 10^-5 The standard form is 6.784 × 10^-5. c) 0.00321 Step 1: Move the decimal point to the right until there is one non-zero digit before the decimal point. 3.21 Step 2: Count the number of places the decimal point was moved. Since it was moved 3 places to the right, the exponent of 10 is -3. 3.21 × 10^-3 The standard form is 3.21 × 10^-3. d) 458754 Step 1: Move the decimal point to the left until there is one non-zero digit before the decimal point. 4.58754 Step 2: Count the number of places the decimal point was moved. Since it was moved 5 places to the left, the exponent of 10 is 5. 4.58754 × 10^5 The standard form is 4.58754 × 10^5. Send me the next one 📸