4. Without using a pocket calculator, calculate the value of the expression

$$
(-5)\left(-\left(\frac{1}{2}+\frac{7}{5}\right)^{0}\right)^{-3}+5^{-2} \cdot\left(2.4 \overline{3}: 10^{-1}+2 \cdot 3^{-1}\right)
$$
4. We note that $\left(\frac{1}{2}+\frac{7}{5}\right)^{0}=1$. The periodic decimal number is written as a simplified fraction $2,4 \overline{3}=\frac{73}{30}$. We calculate $-5 \cdot(-1)^{-3}=5$, and write $5^{-2}=\frac{1}{25}$. We calculate $2,4 \overline{3}: 10^{-1}+2 \cdot 3^{-1}=\frac{73}{30} \cdot 10+\frac{2}{3}=\frac{75}{3}$. We simplify $\frac{1}{25} \cdot \frac{75}{3}=1$ and calculate the value of the expression 6.

![](https://cdn.mathpix.com/cropped/2024_06_07_93a0a0489a8a740fd9e9g-07.jpg?height=77&width=1642&top_left_y=1783&top_left_x=207)

![](https://cdn.mathpix.com/cropped/2024_06_07_93a0a0489a8a740fd9e9g-07.jpg?height=72&width=1639&top_left_y=1837&top_left_x=206)

Calculation of the first product $-5 \cdot(-1)^{-3}=5 \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots$

![](https://cdn.mathpix.com/cropped/2024_06_07_93a0a0489a8a740fd9e9g-07.jpg?height=63&width=1639&top_left_y=1942&top_left_x=206)

Calculation of the last parenthesis $\frac{73}{30} \cdot 10+\frac{2}{3}=\frac{75}{3} \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots$ point

Result.........................................................................................................................