Question

(\frac{x^{2}}{2sqrt{x}})

Explanation:

Assuming the problem is to simplify the expression \(\frac{x^2}{2\sqrt{x}}\), here's the step - by - step solution:

Step 1: Rewrite the square root as a power

Recall that \(\sqrt{x}=x^{\frac{1}{2}}\). So the expression becomes \(\frac{x^{2}}{2x^{\frac{1}{2}}}\).

Step 2: Use the quotient rule of exponents

The quotient rule of exponents states that \(\frac{a^{m}}{a^{n}}=a^{m - n}\) (where \(a
eq0\)). For our expression, \(a = x\), \(m = 2\) and \(n=\frac{1}{2}\). So we have \(\frac{1}{2}x^{2-\frac{1}{2}}\).

Step 3: Simplify the exponent

\(2-\frac{1}{2}=\frac{4 - 1}{2}=\frac{3}{2}\). So the simplified expression is \(\frac{1}{2}x^{\frac{3}{2}}\) or we can also write it as \(\frac{\sqrt{x^{3}}}{2}\) (since \(x^{\frac{3}{2}}=\sqrt{x^{3}}\)) or \(\frac{x\sqrt{x}}{2}\) (because \(\sqrt{x^{3}}=x\sqrt{x}\)).

Answer:

\(\frac{1}{2}x^{\frac{3}{2}}\) (or \(\frac{x\sqrt{x}}{2}\))