Bài 1:
a)\(\left(-6x^3zy\right).\left(\dfrac{2}{3}yx^2\right)^2\)
\(=\) \(\left(-6x^3zy\right).\left(\dfrac{2}{3}\right)^2.y^2\left(x^2\right)^2\)
\(=\)\(\left(-6x^3zy\right).\dfrac{4}{9}y^2x^4\)
\(=\left(-6.\dfrac{4}{9}\right).\left(x^3.x^4\right).\left(y.y^2\right).z\)
\(=-\dfrac{8}{3}x^7.y^3.z\)
- Phần biến: \(x^7.y^3.z\)
- Hệ số: \(-\dfrac{8}{3}\)
b) \(\dfrac{1}{2}x^2.\left(-2x^2y^2z\right).\dfrac{-1}{3}x^2y^3\)
\(=\left(\dfrac{1}{2}-2.\dfrac{-1}{3}\right).\left(x^2.x^2.x^2\right).\left(y^2.y^3\right).z\)
\(=\dfrac{7}{6}x^6y^5z\)
- Phần biến: \(x^6y^5z\)
- Hệ số: \(\dfrac{7}{6}\)
c)\(\left(-2xy^3\right).\left(\dfrac{1}{3}xy\right)^2\)
\(=\) \(\left(-2xy^3\right).\left(\dfrac{1}{3}\right)^2.x^2.y^2\)
\(=\) \(\left(-2xy^3\right).\dfrac{1}{9}.x^2.y^2\)
\(=\left(-2.\dfrac{1}{9}\right).\left(x.x^2\right).\left(y^3.y^2\right)\)
\(=-\dfrac{2}{9}x^3y^5\)
- Phần biến: \(x^3y^5\)
- Hệ số: \(-\dfrac{2}{9}\)
d) \(\dfrac{3}{4}x^4y^5.\dfrac{16}{9}x^2y^3\)
\(=\left(\dfrac{3}{4}.\dfrac{16}{9}\right).\left(x^4.x^2\right).\left(y^5.y^3\right)\)
\(=\dfrac{4}{3}x^6y^8\)
- Phần biến: \(x^6y^8\)
- Hệ số: \(\dfrac{4}{3}\)
e) \(2x^2y^2.\dfrac{1}{4}xy^3.\left(-3xy\right)^2\)
\(=\) \(2x^2y^2.\dfrac{1}{4}xy^3.\left(-3\right)^2.x^2.y^2\)
\(=\) \(2x^2y^2.\dfrac{1}{4}xy^3.9.x^2.y^2\)
\(=\) \((2x^2y^2.9x^2y^2).\dfrac{1}{4}xy^3\)
\(=18x^2y^2.\dfrac{1}{4}xy^3\)
\(=\left(18.\dfrac{1}{4}\right).\left(x^2.x\right).\left(y^2.y^3\right)\)
\(=\dfrac{9}{2}x^3.y^5\)
- Phần biến: \(x^3.y^5\)
- Hệ số: \(\dfrac{9}{2}\)
f) \(\left(-2x^3y\right)^2.xy^2.\dfrac{1}{2}y^5z\)
\(=\) \(\left(-2\right)^2.\left(x^3\right)^2.y^2.xy^2.\dfrac{1}{2}y^5z\)
\(=\) \(4.x^6.y^2.xy^2.\dfrac{1}{2}y^5z\)
\(=\left(4.1.\dfrac{1}{2}\right).\left(x^6.x\right).\left(y^2.y^2.y^5\right).z\)
\(=2x^7y^9z\)
- Phần biến: \(x^7y^9z\)
- Hệ số: \(2\)
g) \(3x^2y^2.\dfrac{1}{9}x^3y.\left(-3xy\right)^2\)
\(=\) \(3x^2y^2.\dfrac{1}{9}x^3y.\left(-3\right)^2.x^2.y^2\)
\(=\) \(3x^2y^2.\dfrac{1}{9}x^3y.9.x^2.y^2\)
\(=\left(3.\dfrac{1}{9}.9\right).\left(x^2.x^3.x^2\right).\left(y^2.y.y^2\right)\)
\(=3x^7y^5\)
- Phần biến: \(x^7y^5\)
- Hệ số: \(3\)
h) \(\left(-4x^3y\right)^2.x^5y^2.\dfrac{1}{8}y^5z\)
\(=\) \(\left(-4\right)^2.\left(x^3\right)^2.y^2.x^5y^2.\dfrac{1}{8}y^5z\)
\(=\) \(16.x^6.y^2.x^5y^2.\dfrac{1}{8}y^5z\)
\(=\left(16.1.\dfrac{1}{8}\right).\left(x^6.x^5\right).\left(y^2.y^2.y^5\right).z\)
\(=2x^{11}y^9z\)
- Phần biến: \(x^{11}y^9z\)
- Hệ số: \(2\)
i) \(\left(-\dfrac{2}{3}xy^2\right).6x^2y^2\)
\(=\left(-\dfrac{2}{3}.6\right).\left(x.x^2\right).\left(y^2.y^2\right)\)
\(=-4x^3y^4\)
- Phần biến: \(x^3y^4\)
- Hệ số: \(-4\)
