((-frac (1)/(2))+(-(1)/(2))^2+(-(1)/(2))^3)((-(3)/(4))cdot (1)/(2))

To solve the expression \(\frac {(-\frac {1}{2})+(-\frac {1}{2})^{2}+(-\frac {1}{2})^{3}}{(-\frac {3}{4})\cdot \frac {1}{2}}\), we need to follow these steps:<br /><br />1. Simplify the numerator.<br />2. Simplify the denominator.<br />3. Divide the simplified numerator by the simplified denominator.<br /><br />Let's start with the numerator:<br />\[ (-\frac{1}{2}) + (-\frac{1}{2})^2 + (-\frac{1}{2})^3 \]<br /><br />Calculate each term separately:<br />\[ (-\frac{1}{2}) = -\frac{1}{2} \]<br />\[ (-\frac{1}{2})^2 = \left(-\frac{1}{2}\right) \times \left(-\frac{1}{2}\right) = \frac{1}{4} \]<br />\[ (-\frac{1}{2})^3 = \left(-\frac{1}{2}\right) \times \left(-\frac{1}{2}\right) \times \left(-\frac{1}{2}\right) = -\frac{1}{8} \]<br /><br />Now, add these terms together:<br />\[ -\frac{1}{2} + \frac{1}{4} - \frac{1}{8} \]<br /><br />To add these fractions, we need a common denominator. The least common multiple of 2, 4, and 8 is 8. Convert each fraction to have a denominator of 8:<br />\[ -\frac{1}{2} = -\frac{4}{8} \]<br />\[ \frac{1}{4} = \frac{2}{8} \]<br />\[ -\frac{1}{8} = -\frac{1}{8} \]<br /><br />Now add them:<br />\[ -\frac{4}{8} + \frac{2}{8} - \frac{1}{8} = -\frac{3}{8} \]<br /><br />Next, simplify the denominator:<br />\[ (-\frac{3}{4}) \cdot \frac{1}{2} \]<br /><br />Multiply the fractions:<br />\[ -\frac{3}{4} \times \frac{1}{2} = -\frac{3}{8} \]<br /><br />Now, divide the simplified numerator by the simplified denominator:<br />\[ \frac{-\frac{3}{8}}{-\frac{3}{8}} = 1 \]<br /><br />Therefore, the value of the expression is:<br />\[ \boxed{1} \]