Questions: b) 1000 ÷ -500(-2)^2 + 2(100-100)^0(-1)^3 + 1/2 - 2/3

△ Simplify the expression \( 1000 \div -500(-2)^{2}+2(100-100)^{0}(-1)^{3}+\frac{1}{2}-\frac{2}{3} \). ○ Evaluate powers ☼ \( (-2)^2 = 4 \), \( (100-100)^0 = 1 \), \( (-1)^3 = -1 \). ○ Substitute evaluated powers ☼ The expression becomes \( 1000 \div -500(4)+2(1)(-1)+\frac{1}{2}-\frac{2}{3} \). ○ Perform division ☼ \( 1000 \div -500 = -2 \). ○ Substitute division result ☼ The expression becomes \( -2(4)+2(1)(-1)+\frac{1}{2}-\frac{2}{3} \). ○ Perform multiplications ☼ \( -2(4) = -8 \), \( 2(1)(-1) = -2 \). ○ Substitute multiplication results ☼ The expression becomes \( -8 -2 + \frac{1}{2} - \frac{2}{3} \). ○ Combine integers ☼ \( -8 - 2 = -10 \). ○ Rewrite expression ☼ The expression becomes \( -10 + \frac{1}{2} - \frac{2}{3} \). ○ Find common denominator ☼ The least common denominator for \( \frac{1}{2} \) and \( \frac{2}{3} \) is 6. ○ Convert fractions ☼ \( \frac{1}{2} = \frac{3}{6} \), \( \frac{2}{3} = \frac{4}{6} \). ○ Substitute converted fractions ☼ The expression becomes \( -10 + \frac{3}{6} - \frac{4}{6} \). ○ Combine fractions ☼ \( \frac{3}{6} - \frac{4}{6} = \frac{-1}{6} \). ○ Substitute fraction result ☼ The expression becomes \( -10 - \frac{1}{6} \). ○ Convert integer to fraction ☼ \( -10 = -\frac{60}{6} \). ○ Rewrite expression ☼ The expression becomes \( -\frac{60}{6} - \frac{1}{6} \). ○ Combine fractions ☼ \( -\frac{60}{6} - \frac{1}{6} = \frac{-61}{6} \). ✧ The final answer is \( -\frac{61}{6} \). ☺ -2, 4, 1, -1, -8, -2, -10, 3/6, 4/6, -1/6, -60/6, -61/6