https://file.aiquickdraw.com/mathbot/file/1729482669084rmbsfmp5.jpg

Let's simplify the given expression:

\[
\frac{x^{\frac{3}{8}}}{\sqrt[4]{x}}.
\]

### Step-by-step simplification:

1. **Rewrite the radical as an exponent**: The denominator has a fourth root, which can be written as an exponent:
   \[
   \sqrt[4]{x} = x^{\frac{1}{4}}.
   \]
   So, the expression becomes:
   \[
   \frac{x^{\frac{3}{8}}}{x^{\frac{1}{4}}}.
   \]

2. **Use the quotient rule of exponents**: When dividing terms with the same base, subtract the exponents:
   \[
   x^{\frac{3}{8} - \frac{1}{4}}.
   \]

3. **Find the common denominator**: The common denominator between \( \frac{3}{8} \) and \( \frac{1}{4} \) is 8:
   \[
   \frac{1}{4} = \frac{2}{8}.
   \]

4. **Perform the subtraction**:
   \[
   \frac{3}{8} - \frac{2}{8} = \frac{1}{8}.
   \]

5. **Final simplified expression**:
   \[
   x^{\frac{1}{8}}.
   \]

Thus, the simplified expression is \( x^{\frac{1}{8}} \).

Would you like more details or have any other questions?

### Related Questions:
1. How do you simplify expressions with fractional exponents?
2. What is the quotient rule for exponents?
3. How do you convert a radical expression to an expression with exponents?
4. How can you add and subtract exponents with different denominators?
5. What are some examples of using the power rule of exponents?

### Tip:
Always convert radicals to exponents when simplifying, as this makes it easier to apply the exponent rules!

Simplify the expression: (x^(3/8)) / (4th root of x). Express your answer so that only positive exponents occur.

Learn how to simplify the expression (x^(3/8)) divided by the 4th root of x. This solution uses key algebraic rules including the quotient rule of exponents and exponent-radical conversion, making it suitable for students in Grades 9-11.

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