B) \( \left( \frac{1}{2} \right)^3 - \left( -\frac{1}{2} \right)^2 : \left( \frac{2}{3} \right)^3 \)

Решение:

1. Первое действие: возведение в степень.
\(\documentclass{article}\) \(\usepackage{amsmath}\) \(\begin{document}\) \(\begin{equation*}\) \(\left\)\(\frac{1}{2} \right\)^3 = \(\frac{1^3}{2^3}\) = \(\frac{1}{8}\) \(\end{equation*}\) \(\end{document}\)

Второе действие: возведение в степень.

\(\documentclass{article}\) \(\usepackage{amsmath}\) \(\begin{document}\) \(\begin{equation*}\) \(\left\)\(-\frac{1}{2} \right\)^2 = \(\frac{(-1)^2}{2^2}\) = \(\frac{1}{4}\) \(\end{equation*}\) \(\end{document}\)

Третье действие: возведение в степень.

\(\documentclass{article}\) \(\usepackage{amsmath}\) \(\begin{document}\) \(\begin{equation*}\) \(\left\)\(\frac{2}{3} \right\)^3 = \(\frac{2^3}{3^3}\) = \(\frac{8}{27}\) \(\end{equation*}\) \(\end{document}\)

Четвёртое действие: деление.

\(\documentclass{article}\) \(\usepackage{amsmath}\) \(\begin{document}\) \(\begin{equation*}\) \(\frac{1}{4}\) : \(\frac{8}{27}\) = \(\frac{1}{4}\) \(\cdot\) \(\frac{27}{8}\) = \(\frac{27}{32}\) \(\end{equation*}\) \(\end{document}\)

Пятое действие: вычитание.

\(\documentclass{article}\) \(\usepackage{amsmath}\) \(\begin{document}\) \(\begin{equation*}\) \(\frac{1}{8}\) - \(\frac{27}{32}\) = \(\frac{4}{32}\) - \(\frac{27}{32}\) = \(\frac{4 - 27}{32}\) = -\(\frac{23}{32}\) \(\end{equation*}\) \(\end{document}\)

Ответ: $$ -\frac{23}{32} $$.