rewrite in simplest rational exponent form $sqrt{x}cdotsqrt4{x}$. show each step of your process.

Explanation:

Step1: Convert square - root to exponent

Recall that $\sqrt{x}=x^{\frac{1}{2}}$ and $\sqrt[4]{x}=x^{\frac{1}{4}}$. So, $\sqrt{x}\cdot\sqrt[4]{x}=x^{\frac{1}{2}}\cdot x^{\frac{1}{4}}$.

Step2: Use exponent - multiplication rule

According to the rule $a^m\cdot a^n=a^{m + n}$, when $a = x$, $m=\frac{1}{2}$, and $n=\frac{1}{4}$, we have $x^{\frac{1}{2}}\cdot x^{\frac{1}{4}}=x^{\frac{1}{2}+\frac{1}{4}}$.

Step3: Add the fractions

Calculate $\frac{1}{2}+\frac{1}{4}=\frac{2 + 1}{4}=\frac{3}{4}$. So, $x^{\frac{1}{2}+\frac{1}{4}}=x^{\frac{3}{4}}$.

Answer:

$x^{\frac{3}{4}}$