B4. Calculate exactly, without using a pocket calculator: $\frac{(-2)^{-3}}{(-0.2)^{3}}-\left(\frac{2}{5}\right)^{-3} \cdot(-3)^{-2} \cdot 0.1^{-1}$.

## PROBLEMS FOR THE THIRD YEAR

Before you are two sets of problems. Problems 1 to 6 of the first set are solved by selecting the correct answer from the five proposed answers and writing it in the table below the corresponding number. Only one answer is correct. A correct answer will be scored with two points, while a wrong answer will result in the deduction of one point.

Problems 1 to 4 of the second set are solved on the attached paper. The solution to each of these problems will be evaluated on a scale from 0 to 6 points. Write only your code on the sheets where you will solve the problems. Write your solution clearly and legibly with a pen.

The time allowed for solving is 90 minutes.

THE NATIONAL COMPETITION COMMITTEE WISHES YOU GREAT SUCCESS.

![](https://cdn.mathpix.com/cropped/2024_06_07_ce887fced8b2a2bf0894g-06.jpg?height=168&width=485&top_left_y=904&top_left_x=800)

## PART I
B4. We calculate: $\frac{(-2)^{-3}}{(-0.2)^{3}}-\left(\frac{2}{5}\right)^{-3} \cdot(-3)^{-2} \cdot 0.1^{-1}=\frac{-\frac{1}{8}}{-\frac{1}{125}}-\frac{125}{8} \cdot \frac{1}{9} \cdot 10=\frac{125}{8} \cdot\left(1-\frac{10}{9}\right)=$ $-\frac{1}{9} \cdot \frac{125}{8}=-\frac{125}{72}$.

![](https://cdn.mathpix.com/cropped/2024_06_07_ce887fced8b2a2bf0894g-13.jpg?height=134&width=1642&top_left_y=447&top_left_x=273)

![](https://cdn.mathpix.com/cropped/2024_06_07_ce887fced8b2a2bf0894g-13.jpg?height=109&width=1642&top_left_y=548&top_left_x=273)

![](https://cdn.mathpix.com/cropped/2024_06_07_ce887fced8b2a2bf0894g-13.jpg?height=60&width=1639&top_left_y=644&top_left_x=274)
Elimination of a double fraction .................................................................................................................

Expanding to a common denominator .................................................................................... 1 .

![](https://cdn.mathpix.com/cropped/2024_06_07_ce887fced8b2a2bf0894g-13.jpg?height=109&width=1642&top_left_y=785&top_left_x=273)

## Third Year

I. PART

| Task | A1 | A2 | A3 | A4 | A5 | A6 |
| :--- | ---: | ---: | ---: | ---: | ---: | ---: |
| Answer | D | C | B | B | A | C |