Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

1. \(\dfrac{x^{\frac{-5}{3}}}{x^{1}}\)
2. \(\dfrac{y^{\frac{4}{3}}}{y^{\frac{1}{5}}}\)
3. \(\dfrac{y^{1}}{y^{\frac{1}{5}}}\)
4. \(\dfrac{y^{\frac{-4}{5}}}{y^{\frac{1}{6}}}\)
5. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{2}{3}}}\)
6. \(\dfrac{x^{1}}{x^{\frac{-5}{2}}}\)
7. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{-5}{3}}}\)
8. \(\dfrac{x^{\frac{3}{4}}}{x^{\frac{-1}{2}}}\)
9. \(\dfrac{y^{\frac{-3}{5}}}{y^{\frac{-2}{5}}}\)
10. \(\dfrac{a^{\frac{-2}{5}}}{a^{\frac{-1}{3}}}\)
11. \(\dfrac{a^{\frac{-4}{3}}}{a^{\frac{1}{5}}}\)
12. \(\dfrac{x^{\frac{-4}{3}}}{x^{\frac{3}{4}}}\)

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-5}{3}}}{x^{1}}\\= x^{ \frac{-5}{3} - 1 }= x^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ x^{8} }}\\=\frac{1}{x^{2}.\sqrt[3]{ x^{2} }}=\frac{1}{x^{2}.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{3}}\\---------------\)
2. \(\dfrac{y^{\frac{4}{3}}}{y^{\frac{1}{5}}}\\= y^{ \frac{4}{3} - \frac{1}{5} }= y^{\frac{17}{15}}\\=\sqrt[15]{ y^{17} }=y.\sqrt[15]{ y^{2} }\\---------------\)
3. \(\dfrac{y^{1}}{y^{\frac{1}{5}}}\\= y^{ 1 - \frac{1}{5} }= y^{\frac{4}{5}}\\=\sqrt[5]{ y^{4} }\\---------------\)
4. \(\dfrac{y^{\frac{-4}{5}}}{y^{\frac{1}{6}}}\\= y^{ \frac{-4}{5} - \frac{1}{6} }= y^{\frac{-29}{30}}\\=\frac{1}{\sqrt[30]{ y^{29} }}=\frac{1}{\sqrt[30]{ y^{29} }}. \color{purple}{\frac{\sqrt[30]{ y }}{\sqrt[30]{ y }}} \\=\frac{\sqrt[30]{ y }}{|y|}\\---------------\)
5. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{2}{3}}}\\= a^{ \frac{-2}{3} - \frac{2}{3} }= a^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ a^{4} }}\\=\frac{1}{a.\sqrt[3]{ a }}=\frac{1}{a.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{2}}\\---------------\)
6. \(\dfrac{x^{1}}{x^{\frac{-5}{2}}}\\= x^{ 1 - (\frac{-5}{2}) }= x^{\frac{7}{2}}\\= \sqrt{ x^{7} } =|x^{3}|. \sqrt{ x } \\---------------\)
7. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{-5}{3}}}\\= y^{ \frac{-1}{2} - (\frac{-5}{3}) }= y^{\frac{7}{6}}\\=\sqrt[6]{ y^{7} }=|y|.\sqrt[6]{ y }\\---------------\)
8. \(\dfrac{x^{\frac{3}{4}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{3}{4} - (\frac{-1}{2}) }= x^{\frac{5}{4}}\\=\sqrt[4]{ x^{5} }=|x|.\sqrt[4]{ x }\\---------------\)
9. \(\dfrac{y^{\frac{-3}{5}}}{y^{\frac{-2}{5}}}\\= y^{ \frac{-3}{5} - (\frac{-2}{5}) }= y^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ y }}=\frac{1}{\sqrt[5]{ y }}. \color{purple}{\frac{\sqrt[5]{ y^{4} }}{\sqrt[5]{ y^{4} }}} \\=\frac{\sqrt[5]{ y^{4} }}{y}\\---------------\)
10. \(\dfrac{a^{\frac{-2}{5}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{-2}{5} - (\frac{-1}{3}) }= a^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ a }}=\frac{1}{\sqrt[15]{ a }}. \color{purple}{\frac{\sqrt[15]{ a^{14} }}{\sqrt[15]{ a^{14} }}} \\=\frac{\sqrt[15]{ a^{14} }}{a}\\---------------\)
11. \(\dfrac{a^{\frac{-4}{3}}}{a^{\frac{1}{5}}}\\= a^{ \frac{-4}{3} - \frac{1}{5} }= a^{\frac{-23}{15}}\\=\frac{1}{\sqrt[15]{ a^{23} }}\\=\frac{1}{a.\sqrt[15]{ a^{8} }}=\frac{1}{a.\sqrt[15]{ a^{8} }} \color{purple}{\frac{\sqrt[15]{ a^{7} }}{\sqrt[15]{ a^{7} }}} \\=\frac{\sqrt[15]{ a^{7} }}{a^{2}}\\---------------\)
12. \(\dfrac{x^{\frac{-4}{3}}}{x^{\frac{3}{4}}}\\= x^{ \frac{-4}{3} - \frac{3}{4} }= x^{\frac{-25}{12}}\\=\frac{1}{\sqrt[12]{ x^{25} }}\\=\frac{1}{|x^{2}|.\sqrt[12]{ x }}=\frac{1}{|x^{2}|.\sqrt[12]{ x }} \color{purple}{\frac{\sqrt[12]{ x^{11} }}{\sqrt[12]{ x^{11} }}} \\=\frac{\sqrt[12]{ x^{11} }}{|x^{3}|}\\---------------\)