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
a) Express 72 as a product of its prime factors in index form. Step 1: Find the prime factors of 72. 72 = 2 × 36 36 = 2 × 18 18 = 2 × 9 9 = 3 × 3 So, 72 = 2 × 2 × 2 × 3 × 3. Step 2: Write the prime factors in index form. 72 = 2^3 × 3^2 The prime factorization of 72 in index form is 2^3 × 3^2. b) Hence or otherwise evaluate the values of x and y in 2^2x × 3^3y = 72. Step 1: Substitute the prime factorization of 72 from part (a) into the equation. 2^2x × 3^3y = 2^3 × 3^2 Step 2: Equate the exponents of the corresponding prime bases. For base 2: 2x = 3 For base 3: 3y = 2 Step 3: Solve for x. x = (3)/(2) Step 4: Solve for y. y = (2)/(3) The values are x = (3)/(2) and y = (2)/(3). That's 2 down. 3 left today — send the next one.