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:

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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.