Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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