To express \( 5 \sqrt[3]{81} \) in fraction form, let's first find the cube root of 81 in its simplest fractional form.

### Step-by-Step Solution:

1. **Break Down 81**:
   \[
   81 = 3^4
   \]
   We want to find the cube root of 81:
   \[
   \sqrt[3]{81} = \sqrt[3]{3^4}
   \]
   This simplifies to:
   \[
   \sqrt[3]{3^4} = 3^{4/3}
   \]
   \( 3^{4/3} \) can be written as:
   \[
   3 \times \sqrt[3]{3}
   \]

2. **Multiply by 5**:
   Now, multiply this by 5:
   \[
   5 \times 3 \times \sqrt[3]{3} = 15 \times \sqrt[3]{3}
   \]
   This is the simplified exact form of the expression in terms of fractions.

### Final Answer:
\[
5 \sqrt[3]{81} = 15 \times \sqrt[3]{3}
\]

This is the expression in its simplest fractional form.

Would you like a further breakdown or have any other questions?

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**Related Questions:**

1. What is \( 5 \times \sqrt[3]{27} \) in exact form?
2. How do you simplify \( \sqrt[3]{243} \) into fractional form?
3. What is the exact form of \( 4 \times \sqrt[3]{32} \)?
4. How do you express \( \sqrt[3]{16} \) in fractional form?
5. What is the simplified form of \( 6 \times \sqrt[3]{54} \)?

**Tip**: When dealing with cube roots of numbers, try expressing the number as a power of a base for easier simplification.

Learn how to express 5 times the cube root of 81 in its simplest fractional form with a step-by-step solution. This problem involves cube roots, exponents, and multiplication of radicals, suitable for high school students.

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