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
Let's solve the problems from the image. Problem 1: Work out (5^4)/(5^4) Step 1: Apply the rule of exponents for division, which states that (a^m)/(a^n) = a^m-n. (5^4)/(5^4) = 5^4-4 Step 2: Simplify the exponent. 5^4-4 = 5^0 Step 3: Any non-zero number raised to the power of 0 is 1. 5^0 = 1 The value is 1. Problem 2: Determine the equation of the line passing through (6, 4) and (2, 0) Step 1: Calculate the slope (m) of the line using the formula m = (y_2 - y_1)/(x_2 - x_1). Let (x_1, y_1) = (6, 4) and (x_2, y_2) = (2, 0). m = (0 - 4)/(2 - 6) m = (-4)/(-4) m = 1 Step 2: Use the slope-intercept form of a linear equation, y = mx + c. Substitute the slope m=1 into the equation. y = 1x + c y = x + c Step 3: Substitute one of the points into the equation to find the y-intercept (c). Let's use point (2, 0). 0 = 2 + c c = 0 - 2 c = -2 Step 4: Write the final equation of the line using the calculated slope and y-intercept. y = x - 2 The equation of the line is y = x - 2. What's next?