1. 問題の内容
与えられた数式を計算し、それぞれの値を求めます。以下に問題の一覧を示します。
1. $(-2)^3$
2. $-2^3$
3. $-(-2^2)$
4. $(-2^2)^3$
5. $\{(-2)^2\}^3$
6. $(-0.1)^3$
7. $(-3 \times 2)^3$
8. $(-3)^2 \times (-3^2)$
9. $(-3)^2 \times (-2)^3$
1
0. $(-6)^3 \div (-2)^4$
1
1. $(-4)^2 \div (-2)^3$
1
2. $(-\frac{1}{3})^2 \times (\frac{3}{2})^3$
1
3. $(-\frac{3}{4})^3 \times (\frac{2}{5})^2$
1
4. $(-\frac{2}{3})^2 \div (-\frac{1}{2})^3$
1
5. $(-\frac{4}{5})^3 \div (-\frac{2}{5})^2$
2. 解き方の手順
各数式について、以下の手順で計算を行います。
1. $(-2)^3 = -2 \times -2 \times -2 = -8$
2. $-2^3 = -(2 \times 2 \times 2) = -8$
3. $-(-2^2) = -(-(2 \times 2)) = -(-4) = 4$
4. $(-2^2)^3 = (-4)^3 = -4 \times -4 \times -4 = -64$
5. $\{(-2)^2\}^3 = (4)^3 = 4 \times 4 \times 4 = 64$
6. $(-0.1)^3 = -0.1 \times -0.1 \times -0.1 = -0.001$
7. $(-3 \times 2)^3 = (-6)^3 = -6 \times -6 \times -6 = -216$
8. $(-3)^2 \times (-3^2) = 9 \times (-9) = -81$
9. $(-3)^2 \times (-2)^3 = 9 \times (-8) = -72$
1
0. $(-6)^3 \div (-2)^4 = -216 \div 16 = -\frac{216}{16} = -\frac{54}{4} = -\frac{27}{2} = -13.5$
1
1. $(-4)^2 \div (-2)^3 = 16 \div (-8) = -2$
1
2. $(-\frac{1}{3})^2 \times (\frac{3}{2})^3 = \frac{1}{9} \times \frac{27}{8} = \frac{27}{72} = \frac{3}{8}$
1
3. $(-\frac{3}{4})^3 \times (\frac{2}{5})^2 = -\frac{27}{64} \times \frac{4}{25} = -\frac{108}{1600} = -\frac{27}{400}$
1
4. $(-\frac{2}{3})^2 \div (-\frac{1}{2})^3 = \frac{4}{9} \div (-\frac{1}{8}) = \frac{4}{9} \times (-8) = -\frac{32}{9}$
1
5. $(-\frac{4}{5})^3 \div (-\frac{2}{5})^2 = -\frac{64}{125} \div \frac{4}{25} = -\frac{64}{125} \times \frac{25}{4} = -\frac{1600}{500} = -\frac{16}{5}$
3. 最終的な答え
1. $-8$
2. $-8$
3. $4$
4. $-64$
5. $64$
6. $-0.001$
7. $-216$
8. $-81$
9. $-72$
1
0. $-\frac{27}{2}$
1
1. $-2$
1
2. $\frac{3}{8}$
1
3. $-\frac{27}{400}$
1
4. $-\frac{32}{9}$
1