Simplify the expression: (2/10)^5 * 10^6 - (4/9)^3 * 182^(1/4)

The expression to simplify is:

\[ \left(\frac{2}{10}\right)^{5} \cdot 10^{6} - \left(\frac{4}{9}\right)^{3} \cdot 182^{\frac{1}{4}} \]

First, simplify the terms:

• \[ \left(\frac{2}{10}\right)^{5} = \left(\frac{1}{5}\right)^{5} = \frac{1}{5^5} = \frac{1}{3125} \]
• \[ \left(\frac{4}{9}\right)^{3} = \frac{4^3}{9^3} = \frac{64}{729} \]

Now substitute these back into the expression:

\[ \frac{1}{3125} \cdot 10^{6} - \frac{64}{729} \cdot 182^{\frac{1}{4}} \]

Calculate the first term:

\[ \frac{1}{3125} \cdot 1000000 = \frac{1000000}{3125} = 320 \]

The second term involves a fourth root of 182, which does not simplify to a rational number. Therefore, the expression cannot be simplified to a single numerical value without approximation or leaving it in a form with roots.

Given the format of the input and the context of typical math problems, it is possible there is a misunderstanding or a typo in the problem. However, based on the provided mathematical expression:

\[ 320 - \frac{64}{729} \cdot \sqrt[4]{182} \]

If we are to provide a numerical answer, we would need to approximate \( \sqrt[4]{182} \). \( 3^4 = 81 \) and \( 4^4 = 256 \), so \( \sqrt[4]{182} \) is between 3 and 4, approximately 3.67.

\[ \frac{64}{729} \cdot 3.67 \approx 0.32 \]

\[ 320 - 0.32 \approx 319.68 \]

However, without further clarification or context that suggests approximation is intended, the exact form is the most accurate answer.

Ответ: 320 - rac{64}{729} ext{∜182}