## 1. 問題の内容

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1. 問題の内容

画像の問題(7)から(12)を解きます。

(7) $(4x)^3 \div (-6x)^2$

(8) $\frac{3}{4}x^2 \div \frac{2}{3}x$

(9) $4a \times (-9ab) \div 6a^2$

(10) $3x \div 6xy \times (-2x)^2$

(11) $14x^2y \times (-3xy^2)^2 \div 21x^4y$

(12) $-24a \div \frac{3}{7}a \times (-\frac{1}{8}b)$

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2. 解き方の手順

(7)

$(4x)^3 \div (-6x)^2 = \frac{(4x)^3}{(-6x)^2} = \frac{64x^3}{36x^2} = \frac{16x}{9}$

(8)

$\frac{3}{4}x^2 \div \frac{2}{3}x = \frac{3}{4}x^2 \times \frac{3}{2x} = \frac{9x^2}{8x} = \frac{9}{8}x$

(9)

$4a \times (-9ab) \div 6a^2 = \frac{4a \times (-9ab)}{6a^2} = \frac{-36a^2b}{6a^2} = -6b$

(10)

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

(11)

$14x^2y \times (-3xy^2)^2 \div 21x^4y = 14x^2y \times (9x^2y^4) \div 21x^4y = \frac{14x^2y \times 9x^2y^4}{21x^4y} = \frac{126x^4y^5}{21x^4y} = 6y^4$

(12)

$-24a \div \frac{3}{7}a \times (-\frac{1}{8}b) = -24a \times \frac{7}{3a} \times (-\frac{1}{8}b) = \frac{-24a \times 7 \times (-b)}{3a \times 8} = \frac{168ab}{24a} = 7b$

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3. 最終的な答え

(7) $\frac{16}{9}x$

(8) $\frac{9}{8}x$

(9) $-6b$

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

(11) $6y^4$

(12) $7b$