問題
次の計算をしなさい。
- (1) \(9x^4y^3\div(-\dfrac{3}{5}xy^2)^3\times\dfrac{y^3}{10}\)
\(\\\) - (2) \((\dfrac{5}{2}xy^2)^3\div\dfrac{5}{8}x^2y^3\times(\dfrac{2}{5}xy)^2\)
\(\\\) - (3) \((\dfrac{a^2b^3}{2})^3\times(-\dfrac{2a^2b}{3})^2\div\dfrac{2a^8b^7}{27}\)
\(\\\) - (4) \((-\dfrac{2}{3}x^3y)^3\div(-\dfrac{1}{6}x^2y^3)^2\times(-\dfrac{3}{2}y)^5\)
\(\\\) - (5) \(18a^3bc^2\div(-\dfrac{2}{3}a^2bc^3)^2\times(-\dfrac{1}{3}ab^2c)^3\)
\(\\\) - (6) \(\dfrac{1}{9}a^5b^6\div(\dfrac{1}{6}a^2b)^2+3ab\times(-2b)^3\)
\(\\\)
解説
マイナスと指数に注意して計算すると、
- (1) \(9x^4y^3\div(-\dfrac{3}{5}xy^2)^3\times\dfrac{y^3}{10}\)
\(\\\)
\(=9x^4y^3\times(-\dfrac{125}{27x^3y^6})\times\dfrac{y^3}{10}\)
\(\\\)
\(=-\dfrac{25}{6}x\)
\(\\\) - (2) \((\dfrac{5}{2}xy^2)^3\div\dfrac{5}{8}x^2y^3\times(\dfrac{2}{5}xy)^2\)
\(\\\)
\(=(\dfrac{125}{8}x^3y^6)\times\dfrac{8}{5x^2y^3}\times(\dfrac{4}{25}x^2y^2)\)
\(\\\)
\(=4x^3y^5\)
\(\\\) - (3) \((\dfrac{a^2b^3}{2})^3\times(-\dfrac{2a^2b}{3})^2\div\dfrac{2a^8b^7}{27}\)
\(\\\)
\(=\dfrac{a^6b^9}{8}\times\dfrac{4a^4b^2}{9}\times\dfrac{27}{2a^8b^7}\)
\(\\\)
\(=\dfrac{3}{2}a^2b^4\)
\(\\\) - (4) \((-\dfrac{2}{3}x^3y)^3\div(-\dfrac{1}{6}x^2y^3)^2\times(-\dfrac{3}{2}y)^5\)
\(\\\)
\(=-\dfrac{8}{27}x^9y^3\times\dfrac{36}{x^4y^6}\times(-\dfrac{243}{32}y^5)\)
\(\\\)
\(=81x^5y^2\)
\(\\\) - (5) \(18a^3bc^2\div(-\dfrac{2}{3}a^2bc^3)^2\times(-\dfrac{1}{3}ab^2c)^3\)
\(\\\)
\(=18a^3bc^2\times\dfrac{9}{4a^4b^2c^6}\times(-\dfrac{1}{27}a^3b^6c^3)\)
\(\\\)
\(=-\dfrac{3a^2b^5}{2c}\)
\(\\\) - (6) \(\dfrac{1}{9}a^5b^6\div(\dfrac{1}{6}a^2b)^2+3ab\times(-2b)^3\)
\(\\\)
\(=\dfrac{1}{9}a^5b^6\times\dfrac{36}{a^4b^2}+3ab\times(-8b^3)\)
\(\\\)
\(=4ab^4-24ab^4\)
\(\\\)
\(=-20ab^4\)
となります。
