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
Alright, Chimuka, let's solve this equation. 22 (a) Solve the equation x^(3)/(2) = 8. Step 1: To solve for x, raise both sides of the equation to the power of (2)/(3). This is the reciprocal of the exponent (3)/(2). (x^(3)/(2))^(2)/(3) = 8^(2)/(3) Step 2: Simplify the left side using the power rule (a^m)^n = a^mn. x^(3)/(2) × (2)/(3) = 8^(2)/(3) x^1 = 8^(2)/(3) x = 8^(2)/(3) Step 3: Evaluate 8^(2)/(3). This can be written as ([3]8)^2. First, find the cube root of 8. [3]8 = 2 Step 4: Square the result from Step 3. x = (2)^2 x = 4 The solution to the equation is x=4. Last free one today — make it count tomorrow, or type /upgrade for unlimited.