Question

(\frac{sqrt{x^5}}{sqrt4{x^3}})

Explanation:

Step1: Convert radicals to exponents

Recall that $\sqrt[n]{a^m}=a^{\frac{m}{n}}$. So, $\sqrt{x^5}=x^{\frac{5}{2}}$ and $\sqrt[4]{x^3}=x^{\frac{3}{4}}$.
The expression becomes $\frac{x^{\frac{5}{2}}}{x^{\frac{3}{4}}}$.

Step2: Use exponent rule for division

When dividing with the same base, subtract the exponents: $a^m\div a^n = a^{m - n}$.
So, $x^{\frac{5}{2}-\frac{3}{4}}$. Calculate the exponent: $\frac{5}{2}-\frac{3}{4}=\frac{10}{4}-\frac{3}{4}=\frac{7}{4}$.
The expression is now $x^{\frac{7}{4}}$.

Step3: Convert back to radical form (optional, but to match common forms)

$x^{\frac{7}{4}}=\sqrt[4]{x^7}=x\sqrt[4]{x^3}$ (or keep as $x^{\frac{7}{4}}$). But simplifying $x^7$ as $x^4\cdot x^3$, so $\sqrt[4]{x^4\cdot x^3}=x\sqrt[4]{x^3}$. However, the exponent form $x^{\frac{7}{4}}$ is also simplified.

Answer:

$x^{\frac{7}{4}}$ (or $x\sqrt[4]{x^3}$)