Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{1}{3}}}\\= a^{ \frac{-1}{3} - \frac{1}{3} }= a^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ a^{2} }}=\frac{1}{\sqrt[3]{ a^{2} }}. \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a}\\---------------\)
2. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{-1}{4}}}\\= y^{ \frac{-1}{3} - (\frac{-1}{4}) }= y^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ y }}=\frac{1}{\sqrt[12]{ y }}. \color{purple}{\frac{\sqrt[12]{ y^{11} }}{\sqrt[12]{ y^{11} }}} \\=\frac{\sqrt[12]{ y^{11} }}{|y|}\\---------------\)
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. \(\dfrac{a^{\frac{-2}{5}}}{a^{-1}}\\= a^{ \frac{-2}{5} - (-1) }= a^{\frac{3}{5}}\\=\sqrt[5]{ a^{3} }\\---------------\)
5. \(\dfrac{y^{-1}}{y^{-2}}\\= y^{ -1 - (-2) }= y^{1}\\\\---------------\)
6. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{-1}{6}}}\\= q^{ \frac{-2}{3} - (\frac{-1}{6}) }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
7. \(\dfrac{y^{\frac{3}{2}}}{y^{\frac{-3}{5}}}\\= y^{ \frac{3}{2} - (\frac{-3}{5}) }= y^{\frac{21}{10}}\\=\sqrt[10]{ y^{21} }=|y^{2}|.\sqrt[10]{ y }\\---------------\)
8. \(\dfrac{y^{\frac{-1}{6}}}{y^{\frac{-5}{4}}}\\= y^{ \frac{-1}{6} - (\frac{-5}{4}) }= y^{\frac{13}{12}}\\=\sqrt[12]{ y^{13} }=|y|.\sqrt[12]{ y }\\---------------\)
9. \(\dfrac{x^{1}}{x^{\frac{1}{2}}}\\= x^{ 1 - \frac{1}{2} }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
10. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{1}{2}}}\\= y^{ \frac{-1}{2} - \frac{1}{2} }= y^{-1}\\=\frac{1}{y}\\---------------\)
11. \(\dfrac{y^{\frac{1}{3}}}{y^{\frac{1}{4}}}\\= y^{ \frac{1}{3} - \frac{1}{4} }= y^{\frac{1}{12}}\\=\sqrt[12]{ y }\\---------------\)
12. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{1}{3}}}\\= x^{ \frac{1}{2} - \frac{1}{3} }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)