Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{5}{6}}}\\= q^{ \frac{-1}{2} - \frac{5}{6} }= q^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ q^{4} }}\\=\frac{1}{q.\sqrt[3]{ q }}=\frac{1}{q.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{2}}\\---------------\)
2. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{-3}{5}}}\\= q^{ \frac{-1}{3} - (\frac{-3}{5}) }= q^{\frac{4}{15}}\\=\sqrt[15]{ q^{4} }\\---------------\)
3. \(\dfrac{a^{\frac{3}{4}}}{a^{1}}\\= a^{ \frac{3}{4} - 1 }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
4. \(\dfrac{q^{\frac{-4}{5}}}{q^{\frac{-5}{3}}}\\= q^{ \frac{-4}{5} - (\frac{-5}{3}) }= q^{\frac{13}{15}}\\=\sqrt[15]{ q^{13} }\\---------------\)
5. \(\dfrac{y^{\frac{-4}{3}}}{y^{\frac{1}{2}}}\\= y^{ \frac{-4}{3} - \frac{1}{2} }= y^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ y^{11} }}\\=\frac{1}{|y|.\sqrt[6]{ y^{5} }}=\frac{1}{|y|.\sqrt[6]{ y^{5} }} \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y^{2}|}\\---------------\)
6. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{2}{5}}}\\= a^{ \frac{-1}{2} - \frac{2}{5} }= a^{\frac{-9}{10}}\\=\frac{1}{\sqrt[10]{ a^{9} }}=\frac{1}{\sqrt[10]{ a^{9} }}. \color{purple}{\frac{\sqrt[10]{ a }}{\sqrt[10]{ a }}} \\=\frac{\sqrt[10]{ a }}{|a|}\\---------------\)
7. \(\dfrac{y^{\frac{-1}{5}}}{y^{\frac{1}{2}}}\\= y^{ \frac{-1}{5} - \frac{1}{2} }= y^{\frac{-7}{10}}\\=\frac{1}{\sqrt[10]{ y^{7} }}=\frac{1}{\sqrt[10]{ y^{7} }}. \color{purple}{\frac{\sqrt[10]{ y^{3} }}{\sqrt[10]{ y^{3} }}} \\=\frac{\sqrt[10]{ y^{3} }}{|y|}\\---------------\)
8. \(\dfrac{y^{\frac{3}{2}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{3}{2} - (\frac{-2}{3}) }= y^{\frac{13}{6}}\\=\sqrt[6]{ y^{13} }=|y^{2}|.\sqrt[6]{ y }\\---------------\)
9. \(\dfrac{q^{\frac{-1}{5}}}{q^{-1}}\\= q^{ \frac{-1}{5} - (-1) }= q^{\frac{4}{5}}\\=\sqrt[5]{ q^{4} }\\---------------\)
10. \(\dfrac{a^{\frac{3}{5}}}{a^{\frac{-4}{3}}}\\= a^{ \frac{3}{5} - (\frac{-4}{3}) }= a^{\frac{29}{15}}\\=\sqrt[15]{ a^{29} }=a.\sqrt[15]{ a^{14} }\\---------------\)
11. \(\dfrac{y^{\frac{5}{2}}}{y^{2}}\\= y^{ \frac{5}{2} - 2 }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
12. \(\dfrac{y^{\frac{4}{5}}}{y^{\frac{-1}{6}}}\\= y^{ \frac{4}{5} - (\frac{-1}{6}) }= y^{\frac{29}{30}}\\=\sqrt[30]{ y^{29} }\\---------------\)