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The given expression is:

\[
7 \cdot \sqrt[3]{54} + 2 \cdot \sqrt[3]{128}
\]

We need to simplify each radical and then combine the like terms.

### Step 1: Simplify \( \sqrt[3]{54} \)
The number 54 can be factored as:
\[
54 = 2 \times 3^3
\]
So, we can simplify \( \sqrt[3]{54} \) as:
\[
\sqrt[3]{54} = \sqrt[3]{2 \times 3^3} = 3 \cdot \sqrt[3]{2}
\]

Now, the first term becomes:
\[
7 \cdot 3 \cdot \sqrt[3]{2} = 21 \cdot \sqrt[3]{2}
\]

### Step 2: Simplify \( \sqrt[3]{128} \)
The number 128 can be factored as:
\[
128 = 2^7
\]
So, we can simplify \( \sqrt[3]{128} \) as:
\[
\sqrt[3]{128} = \sqrt[3]{2^7} = 2^2 \cdot \sqrt[3]{2} = 4 \cdot \sqrt[3]{2}
\]

Now, the second term becomes:
\[
2 \cdot 4 \cdot \sqrt[3]{2} = 8 \cdot \sqrt[3]{2}
\]

### Step 3: Combine like terms
Both terms involve \( \sqrt[3]{2} \), so we can combine them:
\[
21 \cdot \sqrt[3]{2} + 8 \cdot \sqrt[3]{2} = (21 + 8) \cdot \sqrt[3]{2} = 29 \cdot \sqrt[3]{2}
\]

### Final Answer:
\[
29 \cdot \sqrt[3]{2}
\]

Would you like more details or have any questions? Here are some related problems:

1. Simplify \( 5 \cdot \sqrt[3]{16} + 3 \cdot \sqrt[3]{32} \).
2. Find the value of \( 2 \cdot \sqrt[3]{250} + 4 \cdot \sqrt[3]{500} \).
3. Simplify \( \sqrt[3]{54} + \sqrt[3]{250} \).
4. Combine \( 9 \cdot \sqrt[3]{27} + 3 \cdot \sqrt[3]{81} \).
5. Simplify \( 6 \cdot \sqrt[3]{500} + 4 \cdot \sqrt[3]{64} \).

**Tip:** When simplifying cube roots, look for the largest perfect cube factor of the number under the radical!

Simplify the radicals and then combine like radicals: 7 * ∛54 + 2 * ∛128.

Learn how to simplify and combine cube roots in expressions like 7 * ∛54 + 2 * ∛128. Follow a step-by-step solution covering cube root simplification and combining like terms. Suitable for Grades 8-10.

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