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.
ScanSolve AI Answer
Here are the solutions to the problems: Question 1 1.1 Step 1: Evaluate the terms in the expression. 2.705(2 + 6.01)^-2.15 - (7.28)/((0.35)^4) = 2.705(8.01)^-2.15 - (7.28)/(0.01500625) Step 2: Calculate the values using a calculator. = 2.705(0.00998993...) - 485.13888... = 0.0270220... - 485.13888... Step 3: Perform the subtraction and round to three decimal places. = -485.11186... = -485.112 1.2 1.2.1 Convert 0.425 to a fraction. Step 1: Write the decimal as a fraction over a power of 10. 0.425 = (425)/(1000) Step 2: Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 25. (425 ÷ 25)/(1000 ÷ 25) = (17)/(40) The simplified fraction is (17)/(40). 1.2.2 Convert 1.513 to a fraction. Step 1: Let x = 1.5131313.... Multiply to isolate the repeating part. 10x = 15.131313... (1) Step 2: Multiply by 100 (since two digits repeat) to shift the decimal past one cycle of the repeating part. 1000x = 1513.131313... (2) Step 3: Subtract equation (1) from equation (2). 1000x - 10x = 1513.1313... - 15.1313... 990x = 1498 Step 4: Solve for x and simplify the fraction. x = (1498)/(990) = (1498 ÷ 2)/(990 ÷ 2) = (749)/(495) The simplified fraction is (749)/(495). 1.2.3 Convert 0.26 to a fraction. Step 1: Let x = 0.262626.... Multiply by 100 (since two digits repeat). 100x = 26.262626... Step 2: Subtract x from 100x. 100x - x = 26.2626... - 0.2626... 99x = 26 Step 3: Solve for x. x = (26)/(99) The simplified fraction is (26)/(99). Question 2 2.1 Simplify sqrt((32x^5y^3)/(2xy)). Step 1: Simplify the expression inside the square root. (32x^5y^3)/(2xy) = (32)/(2) · (x^5)/(x^1) · (y^3)/(y^1) = 16x^5-1y^3-1 = 16x^4y^2 Step 2: Take the square root of the simplified expression. sqrt(16x^4y^2) = sqrt(16) · sqrt(x^4) · sqrt(y^2) = 4x^4/2y^2/2 = 4x^2y The simplified expression is 4x^2y. 2.2 Simplify 4x^3y^2 × 2x^2y^2 × (1)/(4)xy. Step 1: Multiply the numerical coefficients. 4 × 2 × (1)/(4) = 8 × (1)/(4) = 2 Step 2: Multiply the x terms using the rule x^a × x^b = x^a+b. x^3 × x^2 × x^1 = x^3+2+1 = x^6 Step 3: Multiply the y terms using the rule y^a × y^b = y^a+b. y^2 × y^2 × y^1 = y^2+2+1 = y^5 Step 4: Combine the simplified terms. 2x^6y^5 The simplified expression is 2x^6y^5. 2.3 Simplify (a^2b^3(a^3b)^2)/((a^-2)b^2)^-4. Step 1: Simplify the numerator using exponent rules (xy)^n = x^ny^n and x^a x^b = x^a+b. a^2b^3(a^3b)^2 = a^2b^3(a^3 × 2b^1 × 2) = a^2b^3(a^6b^2) = a^2+6b^3+2 = a^8b^5 Step 2: Simplify the denominator using exponent rules $(xy)^ ✂️ _That answer was long and got cut off. Reply continue and I'll finish it._