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 that are clearly visible in the image. Problem 1: (2 × 2 × 2)^(2)/(3) Step 1: Simplify the base of the exponent. (2 × 2 × 2)^(2)/(3) = (2^3)^(2)/(3) Step 2: Apply the exponent rule (a^m)^n = a^mn. (2^3)^(2)/(3) = 2^3 × (2)/(3) = 2^2 Step 3: Calculate the final value. 2^2 = 4 The answer is 4. Problem 2: (2^3)^(2)/(3) Step 1: Apply the exponent rule (a^m)^n = a^mn. (2^3)^(2)/(3) = 2^3 × (2)/(3) = 2^2 Step 2: Calculate the final value. 2^2 = 4 The answer is 4. Problem 3: (2^2)/(4d) Step 1: Calculate the value of the numerator. 2^2 = 4 Step 2: Substitute the value into the expression. (2^2)/(4d) = (4)/(4d) Step 3: Simplify the fraction by canceling the common factor of 4. (4)/(4d) = (1)/(d) The answer is (1)/(d). Problem 4: sqrt(256 × 289) Step 1: Use the property sqrt(ab) = sqrt(a) × sqrt(b). sqrt(256 × 289) = sqrt(256) × sqrt(289) Step 2: Calculate the square roots of the individual numbers. sqrt(256) = 16 sqrt(289) = 17 Step 3: Multiply the results. 16 × 17 = 272 The answer is 272. Problem 5: sqrt((1)/(4 × 17)) Step 1: Use the property sqrt((a)/(b)) = sqrt(a)sqrt(b). sqrt((1)/(4 × 17)) = sqrt(1)sqrt(4 × 17) Step 2: Simplify the numerator and the denominator using sqrt(ab) = sqrt(a) × sqrt(b). sqrt(1) = 1 sqrt(4 × 17) = sqrt(4) × sqrt(17) = 2 sqrt(17) Step 3: Combine the simplified parts. (1)/(2 sqrt(17)) Step 4: Rationalize the denominator by multiplying the numerator and denominator by sqrt(17). (1)/(2 sqrt(17)) × sqrt(17)sqrt(17) = sqrt(17)2 × 17 Step 5: Simplify the denominator. sqrt(17)34 The answer is $sqrt(17)