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
To simplify the expression, we will evaluate the numerator and the denominator separately. Step 1: Simplify the numerator 9^(1)/(2). A fractional exponent of (1)/(2) means taking the square root. 9^(1)/(2) = sqrt(9) = 3 Step 2: Simplify the denominator 27^(2)/(3). A fractional exponent of (2)/(3) means taking the cube root and then squaring the result. 27^(2)/(3) = ([3]27)^2 First, find the cube root of 27: [3]27 = 3 since 3 × 3 × 3 = 27 Now, square the result: 3^2 = 9 So, 27^(2)/(3) = 9. Step 3: Substitute the simplified numerator and denominator back into the original expression. (9^1)/(2)27^(2)/(3) = (3)/(9) Step 4: Simplify the fraction. (3)/(9) = (1)/(3) The simplified expression is (1)/(3). This matches option B. The final answer is B. (1)/(3). Send me the next one 📸