Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{3}{5}}}{a^{\frac{-3}{2}}}\\= a^{ \frac{3}{5} - (\frac{-3}{2}) }= a^{\frac{21}{10}}\\=\sqrt[10]{ a^{21} }=|a^{2}|.\sqrt[10]{ a }\\---------------\)
2. \(\dfrac{y^{\frac{-5}{2}}}{y^{1}}\\= y^{ \frac{-5}{2} - 1 }= y^{\frac{-7}{2}}\\=\frac{1}{ \sqrt{ y^{7} } }\\=\frac{1}{|y^{3}|. \sqrt{ y } }=\frac{1}{|y^{3}|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{4}|}\\---------------\)
3. \(\dfrac{q^{\frac{-3}{2}}}{q^{\frac{-4}{5}}}\\= q^{ \frac{-3}{2} - (\frac{-4}{5}) }= q^{\frac{-7}{10}}\\=\frac{1}{\sqrt[10]{ q^{7} }}=\frac{1}{\sqrt[10]{ q^{7} }}. \color{purple}{\frac{\sqrt[10]{ q^{3} }}{\sqrt[10]{ q^{3} }}} \\=\frac{\sqrt[10]{ q^{3} }}{|q|}\\---------------\)
4. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{-1}{3} - (\frac{-1}{2}) }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
5. \(\dfrac{x^{\frac{-5}{6}}}{x^{\frac{-3}{5}}}\\= x^{ \frac{-5}{6} - (\frac{-3}{5}) }= x^{\frac{-7}{30}}\\=\frac{1}{\sqrt[30]{ x^{7} }}=\frac{1}{\sqrt[30]{ x^{7} }}. \color{purple}{\frac{\sqrt[30]{ x^{23} }}{\sqrt[30]{ x^{23} }}} \\=\frac{\sqrt[30]{ x^{23} }}{|x|}\\---------------\)
6. \(\dfrac{y^{\frac{1}{4}}}{y^{\frac{3}{5}}}\\= y^{ \frac{1}{4} - \frac{3}{5} }= y^{\frac{-7}{20}}\\=\frac{1}{\sqrt[20]{ y^{7} }}=\frac{1}{\sqrt[20]{ y^{7} }}. \color{purple}{\frac{\sqrt[20]{ y^{13} }}{\sqrt[20]{ y^{13} }}} \\=\frac{\sqrt[20]{ y^{13} }}{|y|}\\---------------\)
7. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{1}{5}}}\\= q^{ \frac{2}{3} - \frac{1}{5} }= q^{\frac{7}{15}}\\=\sqrt[15]{ q^{7} }\\---------------\)
8. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{-5}{2}}}\\= y^{ \frac{-1}{2} - (\frac{-5}{2}) }= y^{2}\\\\---------------\)
9. \(\dfrac{a^{\frac{-1}{4}}}{a^{\frac{1}{2}}}\\= a^{ \frac{-1}{4} - \frac{1}{2} }= a^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ a^{3} }}=\frac{1}{\sqrt[4]{ a^{3} }}. \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a|}\\---------------\)
10. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{3}{2}}}\\= a^{ \frac{-1}{2} - \frac{3}{2} }= a^{-2}\\=\frac{1}{a^{2}}\\---------------\)
11. \(\dfrac{q^{\frac{5}{6}}}{q^{\frac{-4}{3}}}\\= q^{ \frac{5}{6} - (\frac{-4}{3}) }= q^{\frac{13}{6}}\\=\sqrt[6]{ q^{13} }=|q^{2}|.\sqrt[6]{ q }\\---------------\)
12. \(\dfrac{a^{-2}}{a^{\frac{1}{3}}}\\= a^{ -2 - \frac{1}{3} }= a^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ a^{7} }}\\=\frac{1}{a^{2}.\sqrt[3]{ a }}=\frac{1}{a^{2}.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{3}}\\---------------\)