Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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