Jawab:[tex]\displaystyle b.)=\frac{3x^2}{5y^4}\:\:\{y\ne0\}[/tex]
Penjelasan:[tex]\displaystyle\frac{x^2y}{2xy^2}\div\frac{5y^3}{6x}\\\\=\frac{x^2y}{2xy^2}\cdot\frac{6x}{5y^3}\\\\=\frac{6}{2\cdot5}\cdot\frac{x(x^2)y}{xy^2(y^3)}\\\\=\frac{3}{5}\cdot\frac{x^1(x^2)y^1}{x^1y^2(y^3)}\\\\=\frac{3}{5}\cdot\frac{\not x^1(x^2)}{\not x^1}\cdot\frac{y^1}{y^2(y^3)}\\\\=\frac{3x^2}{5}\cdot\frac{y^1}{y^2(y^3)}\\\\\because\:\:n^a\cdot n^b=n^{a+b}\\\\\frac{n^a}{n^b}=n^{a-b}\therefore\\\\=\frac{3x^2}{5}\cdot\frac{y^1}{y^{2+3}}\\\\=\frac{3x^2}{5}\cdot\frac{y^1}{y^5}[/tex]
[tex]\displaystyle=\frac{3x^2}{5}\cdot y^{1-5}\\\\=\frac{3x^2}{5}\cdot y^{-4}\\\\\because a^{-n}=\frac{1}{a^n}\therefore\\\\=\frac{3x^2}{5}\cdot\frac{1}{y^4}\\\\=\frac{3x^2}{5y^4}\:\:\{y\ne0\}[/tex]
(xcvi)
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Jawab:
[tex]\displaystyle b.)=\frac{3x^2}{5y^4}\:\:\{y\ne0\}[/tex]
Penjelasan:
[tex]\displaystyle\frac{x^2y}{2xy^2}\div\frac{5y^3}{6x}\\\\=\frac{x^2y}{2xy^2}\cdot\frac{6x}{5y^3}\\\\=\frac{6}{2\cdot5}\cdot\frac{x(x^2)y}{xy^2(y^3)}\\\\=\frac{3}{5}\cdot\frac{x^1(x^2)y^1}{x^1y^2(y^3)}\\\\=\frac{3}{5}\cdot\frac{\not x^1(x^2)}{\not x^1}\cdot\frac{y^1}{y^2(y^3)}\\\\=\frac{3x^2}{5}\cdot\frac{y^1}{y^2(y^3)}\\\\\because\:\:n^a\cdot n^b=n^{a+b}\\\\\frac{n^a}{n^b}=n^{a-b}\therefore\\\\=\frac{3x^2}{5}\cdot\frac{y^1}{y^{2+3}}\\\\=\frac{3x^2}{5}\cdot\frac{y^1}{y^5}[/tex]
[tex]\displaystyle=\frac{3x^2}{5}\cdot y^{1-5}\\\\=\frac{3x^2}{5}\cdot y^{-4}\\\\\because a^{-n}=\frac{1}{a^n}\therefore\\\\=\frac{3x^2}{5}\cdot\frac{1}{y^4}\\\\=\frac{3x^2}{5y^4}\:\:\{y\ne0\}[/tex]
(xcvi)