Pergunta
)^(1)/(3)=square](https://static.questionai.br.com/resource%2Fqaiseoimg%2F202503%2F27sqrt-3z213square-tdarPBtnT40S.jpg?x-oss-process=image/resize,w_558,h_500/quality,q_35/format,webp)
(27sqrt [3](z^2))^(1)/(3)=square
Solução

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RomeuMestre · Tutor por 5 anos
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To simplify the expression (27\sqrt[3]{z^2})^{\frac{1}{3}}, we can follow these steps:
1. **Rewrite the expression inside the parentheses:**
27\sqrt[3]{z^2} = 27 \cdot z^{\frac{2}{3}}
2. **Apply the exponent \frac{1}{3} to the entire expression:**
\left(27 \cdot z^{\frac{2}{3}}\right)^{\frac{1}{3}}
3. **Distribute the exponent \frac{1}{3} to both terms inside the parentheses:**
27^{\frac{1}{3}} \cdot \left(z^{\frac{2}{3}}\right)^{\frac{1}{3}}
4. **Simplify each term separately:**
- For 27^{\frac{1}{3}}:
27^{\frac{1}{3}} = \sqrt[3]{27} = 3
- For \left(z^{\frac{2}{3}}\right)^{\frac{1}{3}}:
\left(z^{\frac{2}{3}}\right)^{\frac{1}{3}} = z^{\left(\frac{2}{3} \cdot \frac{1}{3}\right)} = z^{\frac{2}{9}}
5. **Combine the simplified terms:**
3 \cdot z^{\frac{2}{9}}
Therefore, the simplified form of the given expression is:
\boxed{3z^{\frac{2}{9}}}
1. **Rewrite the expression inside the parentheses:**
27\sqrt[3]{z^2} = 27 \cdot z^{\frac{2}{3}}
2. **Apply the exponent \frac{1}{3} to the entire expression:**
\left(27 \cdot z^{\frac{2}{3}}\right)^{\frac{1}{3}}
3. **Distribute the exponent \frac{1}{3} to both terms inside the parentheses:**
27^{\frac{1}{3}} \cdot \left(z^{\frac{2}{3}}\right)^{\frac{1}{3}}
4. **Simplify each term separately:**
- For 27^{\frac{1}{3}}:
27^{\frac{1}{3}} = \sqrt[3]{27} = 3
- For \left(z^{\frac{2}{3}}\right)^{\frac{1}{3}}:
\left(z^{\frac{2}{3}}\right)^{\frac{1}{3}} = z^{\left(\frac{2}{3} \cdot \frac{1}{3}\right)} = z^{\frac{2}{9}}
5. **Combine the simplified terms:**
3 \cdot z^{\frac{2}{9}}
Therefore, the simplified form of the given expression is:
\boxed{3z^{\frac{2}{9}}}
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