Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{-1}{3} - (\frac{-2}{3}) }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
2. \(\dfrac{x^{\frac{1}{6}}}{x^{\frac{-1}{5}}}\\= x^{ \frac{1}{6} - (\frac{-1}{5}) }= x^{\frac{11}{30}}\\=\sqrt[30]{ x^{11} }\\---------------\)
3. \(\dfrac{y^{\frac{-2}{5}}}{y^{\frac{3}{2}}}\\= y^{ \frac{-2}{5} - \frac{3}{2} }= y^{\frac{-19}{10}}\\=\frac{1}{\sqrt[10]{ y^{19} }}\\=\frac{1}{|y|.\sqrt[10]{ y^{9} }}=\frac{1}{|y|.\sqrt[10]{ y^{9} }} \color{purple}{\frac{\sqrt[10]{ y }}{\sqrt[10]{ y }}} \\=\frac{\sqrt[10]{ y }}{|y^{2}|}\\---------------\)
4. \(\dfrac{x^{\frac{-2}{5}}}{x^{\frac{2}{3}}}\\= x^{ \frac{-2}{5} - \frac{2}{3} }= x^{\frac{-16}{15}}\\=\frac{1}{\sqrt[15]{ x^{16} }}\\=\frac{1}{x.\sqrt[15]{ x }}=\frac{1}{x.\sqrt[15]{ x }} \color{purple}{\frac{\sqrt[15]{ x^{14} }}{\sqrt[15]{ x^{14} }}} \\=\frac{\sqrt[15]{ x^{14} }}{x^{2}}\\---------------\)
5. \(\dfrac{y^{\frac{1}{4}}}{y^{\frac{-5}{6}}}\\= y^{ \frac{1}{4} - (\frac{-5}{6}) }= y^{\frac{13}{12}}\\=\sqrt[12]{ y^{13} }=|y|.\sqrt[12]{ y }\\---------------\)
6. \(\dfrac{a^{-1}}{a^{\frac{2}{5}}}\\= a^{ -1 - \frac{2}{5} }= a^{\frac{-7}{5}}\\=\frac{1}{\sqrt[5]{ a^{7} }}\\=\frac{1}{a.\sqrt[5]{ a^{2} }}=\frac{1}{a.\sqrt[5]{ a^{2} }} \color{purple}{\frac{\sqrt[5]{ a^{3} }}{\sqrt[5]{ a^{3} }}} \\=\frac{\sqrt[5]{ a^{3} }}{a^{2}}\\---------------\)
7. \(\dfrac{x^{\frac{1}{3}}}{x^{\frac{1}{2}}}\\= x^{ \frac{1}{3} - \frac{1}{2} }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
8. \(\dfrac{x^{\frac{4}{3}}}{x^{1}}\\= x^{ \frac{4}{3} - 1 }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
9. \(\dfrac{q^{2}}{q^{-2}}\\= q^{ 2 - (-2) }= q^{4}\\\\---------------\)
10. \(\dfrac{x^{\frac{1}{4}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{1}{4} - (\frac{-1}{3}) }= x^{\frac{7}{12}}\\=\sqrt[12]{ x^{7} }\\---------------\)
11. \(\dfrac{y^{\frac{4}{5}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{4}{5} - (\frac{-2}{3}) }= y^{\frac{22}{15}}\\=\sqrt[15]{ y^{22} }=y.\sqrt[15]{ y^{7} }\\---------------\)
12. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{2}{3}}}\\= q^{ \frac{-1}{3} - \frac{2}{3} }= q^{-1}\\=\frac{1}{q}\\---------------\)