To simplify the given expression [tex]\( \left(\frac{1}{2}\right)^2 - 6\left(2 - \frac{2}{3}\right) \)[/tex], we'll break it down into a step-by-step process:
1. Calculate the first term [tex]\(\left(\frac{1}{2}\right)^2\)[/tex]:
[tex]\[
\left(\frac{1}{2}\right)^2 = \frac{1}{4} = 0.25
\][/tex]
2. Simplify the expression inside the parentheses [tex]\(2 - \frac{2}{3}\)[/tex]:
[tex]\[
2 - \frac{2}{3} = \frac{6}{3} - \frac{2}{3} = \frac{4}{3}
\][/tex]
3. Multiply the simplified expression by [tex]\(-6\)[/tex]:
[tex]\[
-6 \left(\frac{4}{3}\right) = -\frac{24}{3} = -8
\][/tex]
4. Combine the two results (the first term and the second term):
[tex]\[
\left(\frac{1}{2}\right)^2 - 6\left(2 - \frac{2}{3}\right) = 0.25 - 8
\][/tex]
5. Simplify the final expression:
[tex]\[
0.25 - 8 = -7.75
\][/tex]
Thus, the simplified expression is
[tex]\[ \left(\frac{1}{2}\right)^2 - 6\left(2 - \frac{2}{3}\right) = -7.75 \][/tex]
