(27sqrt [3](z^2))^(1)/(3)=square

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:
$$\boxed{3z^{\frac{2}{9}}}$$