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Описание: Final Answer: $\boxed{\frac{10}{3}}$

Solution:
Here we are trying to find the value of $(0.027)^{-\frac{1}{3}}$.

Step 1: First we convert $0.027$ into a fraction:
$$0.027 = \frac{27}{1000}$$
Step 2: Now we apply the power:
$$(0.027)^{-\frac{1}{3}} = \left(\frac{27}{1000}\right)^{-\frac{1}{3}}$$
Step 3: Negative power means taking the reciprocal:
$$= \left(\frac{1000}{27}\right)^{\frac{1}{3}}$$
Step 4: Cube root means taking the cube root of numerator and denominator separately:
$$= \frac{1000^{\frac{1}{3}}}{27^{\frac{1}{3}}}$$
Step 5: We know that $1000 = 10^3$ and $27 = 3^3$, so:
$$= \frac{(10^3)^{\frac{1}{3}}}{(3^3)^{\frac{1}{3}}} = \frac{10}{3}$$
So the final answer is $\boxed{\frac{10}{3}}$.

Explanation:
We solved this problem step-by-step. First we converted the decimal into a fraction, then handled the negative power, and then applied the cube root formula. It became easy because $1000$ and $27$ are perfect cubes.

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