与えられた9つの数式を計算し、最も簡単な形に整理します。

1. 問題の内容

与えられた9つの数式を計算し、最も簡単な形に整理します。

2. 解き方の手順

(1) $a^2b \times b \div a = a^2b^2 \div a = a^{2-1}b^2 = ab^2$

(2) $x^2 \div xy = \frac{x^2}{xy} = \frac{x}{y}$

(3) $4a \times 6b \div 3a = 24ab \div 3a = \frac{24ab}{3a} = 8b$

(4) $10x \div (-5x^2) \times 2x^3 = \frac{10x}{-5x^2} \times 2x^3 = -\frac{2}{x} \times 2x^3 = -4x^2$

(5) $12a^2b^2 \div (-2b)^2 = 12a^2b^2 \div 4b^2 = \frac{12a^2b^2}{4b^2} = 3a^2$

(6) $6x^2y \div \frac{9}{2}y \div (-\frac{4}{3}x) = 6x^2y \times \frac{2}{9y} \times (-\frac{3}{4x})^{-1} = 6x^2y \times \frac{2}{9y} \times (-\frac{3x}{4}) = \frac{12x^2y}{9y} \times (-\frac{3x}{4}) = \frac{4x^2}{3} \times (-\frac{3x}{4}) = -x^3$

(7) $(-2y)^3 \times 3x^2y = (-8y^3) \times 3x^2y = -24x^2y^4$

(8) $-\frac{2}{9}x^2 \div \frac{x^2}{18} = -\frac{2}{9}x^2 \times \frac{18}{x^2} = -\frac{2 \times 18}{9} = -4$

(9) $\frac{1}{4}x^2y^2 \div (-\frac{5}{12}xy^2) = \frac{1}{4}x^2y^2 \times (-\frac{12}{5xy^2}) = -\frac{12x^2y^2}{20xy^2} = -\frac{3x}{5}$

3. 最終的な答え

(1) $ab^2$

(2) $\frac{x}{y}$

(3) $8b$

(4) $-4x^2$

(5) $3a^2$

(6) $-x^3$

(7) $-24x^2y^4$

(8) $-4$

(9) $-\frac{3x}{5}$