Simplify $$ \frac{\sqrt[11]{x^{9}}}{\sqrt[4]{x^{3}}} $$ $$ X^{[?]} $$

Question

UpStudy AI · Accepted Answer

To simplify the expression:

$$
\frac{\sqrt[11]{x^{9}}}{\sqrt[4]{x^{3}}}
$$

Let's rewrite each radical using fractional exponents:

1. **Numerator:** $$\sqrt[11]{x^{9}} = x^{\frac{9}{11}}$$
2. **Denominator:** $$\sqrt[4]{x^{3}} = x^{\frac{3}{4}}$$

Now, divide the two expressions by subtracting the exponents:

$$
x^{\frac{9}{11}} \div x^{\frac{3}{4}} = x^{\frac{9}{11} - \frac{3}{4}}
$$

To subtract the exponents, find a common denominator (which is 44 in this case):

$$
\frac{9}{11} = \frac{36}{44} \quad \text{and} \quad \frac{3}{4} = \frac{33}{44}
$$

Subtracting them:

$$
\frac{36}{44} - \frac{33}{44} = \frac{3}{44}
$$

So, the simplified expression is:

$$
x^{\frac{3}{44}}
$$

**Final Answer:**

$$ X^{\frac{3}{44}} $$
$$ x^{\frac{3}{44}} $$

Simplify