Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{-1}}{x^{\frac{-2}{3}}}\\= x^{ -1 - (\frac{-2}{3}) }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
2. \(\dfrac{y^{\frac{-1}{6}}}{y^{\frac{-4}{5}}}\\= y^{ \frac{-1}{6} - (\frac{-4}{5}) }= y^{\frac{19}{30}}\\=\sqrt[30]{ y^{19} }\\---------------\)
3. \(\dfrac{x^{\frac{-3}{2}}}{x^{\frac{-2}{3}}}\\= x^{ \frac{-3}{2} - (\frac{-2}{3}) }= x^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ x^{5} }}=\frac{1}{\sqrt[6]{ x^{5} }}. \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x|}\\---------------\)
4. \(\dfrac{a^{1}}{a^{\frac{-4}{3}}}\\= a^{ 1 - (\frac{-4}{3}) }= a^{\frac{7}{3}}\\=\sqrt[3]{ a^{7} }=a^{2}.\sqrt[3]{ a }\\---------------\)
5. \(\dfrac{y^{-1}}{y^{\frac{-4}{3}}}\\= y^{ -1 - (\frac{-4}{3}) }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
6. \(\dfrac{a^{\frac{3}{5}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{3}{5} - (\frac{-1}{2}) }= a^{\frac{11}{10}}\\=\sqrt[10]{ a^{11} }=|a|.\sqrt[10]{ a }\\---------------\)
7. \(\dfrac{x^{\frac{-2}{5}}}{x^{\frac{2}{3}}}\\= x^{ \frac{-2}{5} - \frac{2}{3} }= x^{\frac{-16}{15}}\\=\frac{1}{\sqrt[15]{ x^{16} }}\\=\frac{1}{x.\sqrt[15]{ x }}=\frac{1}{x.\sqrt[15]{ x }} \color{purple}{\frac{\sqrt[15]{ x^{14} }}{\sqrt[15]{ x^{14} }}} \\=\frac{\sqrt[15]{ x^{14} }}{x^{2}}\\---------------\)
8. \(\dfrac{x^{1}}{x^{\frac{1}{5}}}\\= x^{ 1 - \frac{1}{5} }= x^{\frac{4}{5}}\\=\sqrt[5]{ x^{4} }\\---------------\)
9. \(\dfrac{x^{\frac{5}{4}}}{x^{\frac{3}{5}}}\\= x^{ \frac{5}{4} - \frac{3}{5} }= x^{\frac{13}{20}}\\=\sqrt[20]{ x^{13} }\\---------------\)
10. \(\dfrac{y^{-1}}{y^{-1}}\\= y^{ -1 - (-1) }= y^{0}\\=1\\---------------\)
11. \(\dfrac{y^{\frac{5}{2}}}{y^{1}}\\= y^{ \frac{5}{2} - 1 }= y^{\frac{3}{2}}\\= \sqrt{ y^{3} } =|y|. \sqrt{ y } \\---------------\)
12. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{-1}{4}}}\\= q^{ \frac{-1}{3} - (\frac{-1}{4}) }= q^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ q }}=\frac{1}{\sqrt[12]{ q }}. \color{purple}{\frac{\sqrt[12]{ q^{11} }}{\sqrt[12]{ q^{11} }}} \\=\frac{\sqrt[12]{ q^{11} }}{|q|}\\---------------\)