Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-5}{2}}}{x^{\frac{5}{6}}}\\= x^{ \frac{-5}{2} - \frac{5}{6} }= x^{\frac{-10}{3}}\\=\frac{1}{\sqrt[3]{ x^{10} }}\\=\frac{1}{x^{3}.\sqrt[3]{ x }}=\frac{1}{x^{3}.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{4}}\\---------------\)
2. \(\dfrac{a^{\frac{5}{6}}}{a^{\frac{1}{2}}}\\= a^{ \frac{5}{6} - \frac{1}{2} }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
3. \(\dfrac{y^{\frac{1}{3}}}{y^{\frac{-3}{5}}}\\= y^{ \frac{1}{3} - (\frac{-3}{5}) }= y^{\frac{14}{15}}\\=\sqrt[15]{ y^{14} }\\---------------\)
4. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{-5}{2}}}\\= a^{ \frac{1}{2} - (\frac{-5}{2}) }= a^{3}\\\\---------------\)
5. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{-1}{3} - (\frac{-1}{2}) }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
6. \(\dfrac{y^{\frac{-4}{3}}}{y^{\frac{5}{3}}}\\= y^{ \frac{-4}{3} - \frac{5}{3} }= y^{-3}\\=\frac{1}{y^{3}}\\---------------\)
7. \(\dfrac{q^{1}}{q^{\frac{5}{6}}}\\= q^{ 1 - \frac{5}{6} }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
8. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{-3}{5}}}\\= x^{ \frac{-1}{3} - (\frac{-3}{5}) }= x^{\frac{4}{15}}\\=\sqrt[15]{ x^{4} }\\---------------\)
9. \(\dfrac{x^{\frac{1}{4}}}{x^{\frac{1}{5}}}\\= x^{ \frac{1}{4} - \frac{1}{5} }= x^{\frac{1}{20}}\\=\sqrt[20]{ x }\\---------------\)
10. \(\dfrac{y^{\frac{-3}{2}}}{y^{2}}\\= y^{ \frac{-3}{2} - 2 }= y^{\frac{-7}{2}}\\=\frac{1}{ \sqrt{ y^{7} } }\\=\frac{1}{|y^{3}|. \sqrt{ y } }=\frac{1}{|y^{3}|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{4}|}\\---------------\)
11. \(\dfrac{q^{\frac{-1}{4}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{-1}{4} - (\frac{-2}{3}) }= q^{\frac{5}{12}}\\=\sqrt[12]{ q^{5} }\\---------------\)
12. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{-2}{3} - (\frac{-1}{2}) }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)