a/ \(\left(-2x^2y\right)5xy^4\)

\(=-10x^3y^5\)

tự lm tiếp, rất dễ

a) Ta có: \(\left(-2x^2y\right)\cdot\left(5xy^4\right)\)

\(=\left(-2\cdot5\right)\cdot\left(x^2\cdot x\right)\cdot\left(y\cdot y^4\right)\)

\(=-10x^3y^5\)

b) Ta có: \(\left(\dfrac{27}{10}x^4y^2\right)\cdot\left(\dfrac{5}{9}xy\right)\)

\(=\left(\dfrac{27}{10}\cdot\dfrac{5}{9}\right)\cdot\left(x^4\cdot x\right)\cdot\left(y^2\cdot y\right)\)

\(=\dfrac{3}{2}x^5y^3\)

c) Ta có: \(\left(\dfrac{1}{3}x^3y\right)\cdot\left(-xy\right)^2\)

\(=\dfrac{1}{3}x^3y\cdot x^2y^2\)

\(=\dfrac{1}{3}x^5y^3\)

Ta có :

x² - y² = 4

\(\frac{x}{5}=\frac{y}{3}\)

Áp dụng tính chất dãy tỉ số bằng nhau , ta có :

\(\frac{x}{5}=\frac{y}{3}=\left(\frac{x}{5}\right)^2=\left(\frac{y}{3}\right)^2=\frac{x^2}{5^2}=\frac{y^2}{3^2}=\frac{x^2-y^2}{5^2-3^2}=\frac{4}{16}=\frac{1}{4}\)

\(\Rightarrow\hept{\begin{cases}x=\frac{1}{4}.5=\frac{5}{4}\\y=\frac{1}{4}.3=\frac{3}{4}\end{cases}}\)

\(\dfrac{x}{5}=\dfrac{y}{4}=\dfrac{z}{2}\)

\(\Rightarrow\dfrac{x^3}{125}=\dfrac{y^3}{64}=\dfrac{z^3}{8}=\dfrac{x^3-y^3+z^3}{125-64+8}=\dfrac{69}{69}=1\)

\(\Rightarrow\left\{{}\begin{matrix}x=\sqrt[3]{125}=5\\y=\sqrt[3]{64}=4\\z=\sqrt[3]{8}=2\end{matrix}\right.\)