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: 12) Simplify: (4s)^3 Step 1: Apply the power of a product rule, (ab)^m = a^m b^m. (4s)^3 = 4^3 s^3 Step 2: Calculate the value of 4^3. = 64s^3 The correct option is A. 13) Rewrite 5^-3 in simplest form. Step 1: Apply the negative exponent rule, a^-n = (1)/(a^n). 5^-3 = (1)/(5^3) The correct option is B. 14) Rewrite (4r)^-2 without a negative exponent. Step 1: Apply the negative exponent rule, a^-n = (1)/(a^n). (4r)^-2 = (1)/((4r)^2) Step 2: Apply the power of a product rule, (ab)^m = a^m b^m, and calculate 4^2. = (1)/(4^2 r^2) = (1)/(16r^2) The correct option is D. 15) Simplify: 2(6h)^-2 Step 1: Apply the negative exponent rule, a^-n = (1)/(a^n), to the term (6h)^-2. 2(6h)^-2 = 2 · (1)/((6h)^2) Step 2: Apply the power of a product rule, (ab)^m = a^m b^m, and calculate 6^2. = 2 · (1)/(6^2 h^2) = 2 · (1)/(36h^2) Step 3: Multiply and simplify the fraction. = (2)/(36h^2) = (1)/(18h^2) The correct option is A. That's 2 down. 3 left today — send the next one.