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
You're on a roll — I can clarify that step for you, ~Mataa🫶🏽! The confusion is in the algebraic manipulation of the exponent. Here's how we go from 10^-(pH_1 - 3) to 10^-pH_1 + 3 and then to 10^-pH_1 × 10^3: Step 1: Distribute the negative sign into the parentheses in the exponent. 10^-(pH_1 - 3) When you distribute the negative sign, it changes the sign of each term inside the parentheses: -(pH_1 - 3) = -pH_1 - (-3) = -pH_1 + 3 So, the expression becomes: 10^-pH_1 + 3 Step 2: Apply the exponent rule a^m+n = a^m × a^n. In our case, a=10, m=-pH_1, and n=3. 10^-pH_1 + 3 = 10^-pH_1 × 10^3 This is a fundamental rule of exponents: when you multiply powers with the same base, you add their exponents. Conversely, an exponent that is a sum can be split into a product of powers. So, the full transformation is: [H_3O^+]_2 = 10^-(pH_1 - 3) [H_3O^+]_2 = 10^-pH_1 + 3 [H_3O^+]_2 = 10^-pH_1 × 10^3 Does that make more sense? Send me the next one 📸