https://file.aiquickdraw.com/mathbot/file/17231185802700tgv85t9.jpg

The expression provided is:

\[
\sqrt[3]{32} - \sqrt[3]{250} + \sqrt[3]{-54}
\]

Let's break it down step by step.

1. **Evaluate each cube root:**
   - \(\sqrt[3]{32} = 2^5 = 2 \times 2 \times 2 \times 2 \times 2 = 32\), so \(\sqrt[3]{32} = 2\).
   - \(\sqrt[3]{250}\) can be broken down into prime factors: \(250 = 2 \times 5^3\). So, \(\sqrt[3]{250} = \sqrt[3]{2 \times 5^3} = 5\sqrt[3]{2}\).
   - \(\sqrt[3]{-54}\) can be broken down into prime factors: \(-54 = -1 \times 2 \times 3^3\). Therefore, \(\sqrt[3]{-54} = -3\sqrt[3]{2}\).

2. **Combine the evaluated terms:**
   \[
   \sqrt[3]{32} - \sqrt[3]{250} + \sqrt[3]{-54} = 2 - 5\sqrt[3]{2} - 3\sqrt[3]{2}
   \]

3. **Simplify the expression:**
   \[
   2 - 8\sqrt[3]{2}
   \]

Thus, the simplified form of the expression is \(2 - 8\sqrt[3]{2}\).

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Learn how to simplify the cube root expression ∛32 - ∛250 + ∛(-54) step-by-step. This problem involves evaluating cube roots and combining terms. Suitable for Grades 7-9 mathematics curriculum.

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