To solve the exercise you can use the following property of powers
[tex](\frac{a}{b})^n=\frac{a^n}{b^n}[/tex]
Then, you have
[tex]\begin{gathered} |(\frac{-1}{2})^3\div(\frac{1}{4})^2|=|\frac{(-1)^3}{(2)^3}^{}\div\frac{(1)^2}{(4)^2}^{}| \\ |(\frac{-1}{2})^3\div(\frac{1}{4})^2|=|\frac{-1^{}}{8}^{}\div\frac{1}{16}^{}| \end{gathered}[/tex]
Now, apply the definition of fractional division, that is
[tex]\frac{a}{b}\div\frac{c}{d}=\frac{a\cdot d}{b\cdot c}[/tex][tex]\begin{gathered} |(\frac{-1}{2})^3\div(\frac{1}{4})^2|=|\frac{-1^{}\cdot16}{8\cdot1}^{}| \\ |(\frac{-1}{2})^3\div(\frac{1}{4})^2|=|\frac{-1^{}6}{8}^{}| \\ |(\frac{-1}{2})^3\div(\frac{1}{4})^2|=|-2| \end{gathered}[/tex]
Finally, apply the definition of absolute value, that is, it is the distance between a number and zero. The distance between -2 and 0 is 2.
Therefore, the value of the expression is 2.
[tex]\begin{gathered} |(\frac{-1}{2})^3\div(\frac{1}{4})^2|=|-2| \\ |(\frac{-1}{2})^3\div(\frac{1}{4})^2|=2 \end{gathered}[/tex]
