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
Step 1: Express all numbers in the equation as powers of their prime factors. The given equation is 9^2y × 2^x = 72. We can write 9 as 3^2. We can write 72 as 8 × 9 = 2^3 × 3^2. Step 2: Substitute these prime factorizations into the equation. (3^2)^2y × 2^x = 2^3 × 3^2 Step 3: Apply the power rule (a^m)^n = a^mn to simplify the left side of the equation. 3^2 × 2y × 2^x = 2^3 × 3^2 3^4y × 2^x = 2^3 × 3^2 Step 4: Equate the exponents of the corresponding bases on both sides of the equation. For base 3: 3^4y = 3^2 This implies that the exponents must be equal: 4y = 2 For base 2: 2^x = 2^3 This implies that the exponents must be equal: x = 3 Step 5: Solve for y. From 4y = 2: y = (2)/(4) y = (1)/(2) The values of x and y are: x=3, y=(1)/(2) 3 done, 2 left today. You're making progress.