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
To rewrite the expression \(sqrt(x) × [4]x\) in simplest rational exponent form, follow these steps: 1. Convert to Exponential Form: The square root of \(x\) can be expressed as \(x^1/2\). The fourth root of \(x\) can be expressed as \(x^1/4\). So, we have: \[ sqrt(x) = x^1/2 and [4]x = x^1/4 \] 2. Multiply the Exponents: Now, multiply the two expressions: \[ x^1/2 × x^1/4 \] 3. Apply the Product of Powers Rule: When multiplying like bases, add the exponents: \[ x^1/2 + 1/4 \] 4. Find a Common Denominator: The common denominator for \(1/2\) and \(1/4\) is \(4\): \[ 1/2 = 2/4 and 1/4 = 1/4 \] 5. Add the Exponents: \[ 2/4 + 1/4 = 3/4 \] 6. Final Expression: Therefore, the expression simplifies to: \[ x^3/4 \] So, the simplest rational exponent form of \(sqrt(x) × [4]x\) is \(x^3/4\).