Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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