Question

$$(x^2)(2sqrt{x})$$

Explanation:

Step1: Rewrite the square root as an exponent

We know that $\sqrt{x} = x^{\frac{1}{2}}$, so the expression becomes $(x^{2})(2x^{\frac{1}{2}})$.

Step2: Use the rule of exponents for multiplication ($a^{m} \cdot a^{n}=a^{m + n}$)

Multiply the coefficients and add the exponents of $x$. The coefficient of $x^{2}$ is 1 and of $2x^{\frac{1}{2}}$ is 2, so $1\times2 = 2$. For the exponents of $x$, we have $2+\frac{1}{2}=\frac{4 + 1}{2}=\frac{5}{2}$. So the expression is $2x^{\frac{5}{2}}$.

Step3: (Optional) Rewrite in radical form if needed

$x^{\frac{5}{2}}=\sqrt{x^{5}}=x^{2}\sqrt{x}$, so $2x^{\frac{5}{2}} = 2x^{2}\sqrt{x}$.

Answer:

$2x^{\frac{5}{2}}$ (or $2x^{2}\sqrt{x}$)