Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{1}}{q^{\frac{-1}{5}}}\\= q^{ 1 - (\frac{-1}{5}) }= q^{\frac{6}{5}}\\=\sqrt[5]{ q^{6} }=q.\sqrt[5]{ q }\\---------------\)
2. \(\dfrac{q^{\frac{-1}{5}}}{q^{\frac{5}{3}}}\\= q^{ \frac{-1}{5} - \frac{5}{3} }= q^{\frac{-28}{15}}\\=\frac{1}{\sqrt[15]{ q^{28} }}\\=\frac{1}{q.\sqrt[15]{ q^{13} }}=\frac{1}{q.\sqrt[15]{ q^{13} }} \color{purple}{\frac{\sqrt[15]{ q^{2} }}{\sqrt[15]{ q^{2} }}} \\=\frac{\sqrt[15]{ q^{2} }}{q^{2}}\\---------------\)
3. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{2}{3}}}\\= y^{ \frac{-1}{3} - \frac{2}{3} }= y^{-1}\\=\frac{1}{y}\\---------------\)
4. \(\dfrac{q^{\frac{-3}{5}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{-3}{5} - (\frac{-2}{3}) }= q^{\frac{1}{15}}\\=\sqrt[15]{ q }\\---------------\)
5. \(\dfrac{a^{\frac{-5}{3}}}{a^{\frac{-5}{4}}}\\= a^{ \frac{-5}{3} - (\frac{-5}{4}) }= a^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ a^{5} }}=\frac{1}{\sqrt[12]{ a^{5} }}. \color{purple}{\frac{\sqrt[12]{ a^{7} }}{\sqrt[12]{ a^{7} }}} \\=\frac{\sqrt[12]{ a^{7} }}{|a|}\\---------------\)
6. \(\dfrac{y^{\frac{1}{3}}}{y^{\frac{2}{5}}}\\= y^{ \frac{1}{3} - \frac{2}{5} }= y^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ y }}=\frac{1}{\sqrt[15]{ y }}. \color{purple}{\frac{\sqrt[15]{ y^{14} }}{\sqrt[15]{ y^{14} }}} \\=\frac{\sqrt[15]{ y^{14} }}{y}\\---------------\)
7. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{5}{6}}}\\= q^{ \frac{-1}{3} - \frac{5}{6} }= q^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ q^{7} }}\\=\frac{1}{|q|.\sqrt[6]{ q }}=\frac{1}{|q|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{2}|}\\---------------\)
8. \(\dfrac{a^{\frac{-1}{4}}}{a^{\frac{2}{5}}}\\= a^{ \frac{-1}{4} - \frac{2}{5} }= a^{\frac{-13}{20}}\\=\frac{1}{\sqrt[20]{ a^{13} }}=\frac{1}{\sqrt[20]{ a^{13} }}. \color{purple}{\frac{\sqrt[20]{ a^{7} }}{\sqrt[20]{ a^{7} }}} \\=\frac{\sqrt[20]{ a^{7} }}{|a|}\\---------------\)
9. \(\dfrac{y^{\frac{-3}{5}}}{y^{\frac{-2}{5}}}\\= y^{ \frac{-3}{5} - (\frac{-2}{5}) }= y^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ y }}=\frac{1}{\sqrt[5]{ y }}. \color{purple}{\frac{\sqrt[5]{ y^{4} }}{\sqrt[5]{ y^{4} }}} \\=\frac{\sqrt[5]{ y^{4} }}{y}\\---------------\)
10. \(\dfrac{a^{\frac{-1}{2}}}{a^{1}}\\= a^{ \frac{-1}{2} - 1 }= a^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ a^{3} } }\\=\frac{1}{|a|. \sqrt{ a } }=\frac{1}{|a|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{2}|}\\---------------\)
11. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{2}{3} - (\frac{-1}{2}) }= y^{\frac{7}{6}}\\=\sqrt[6]{ y^{7} }=|y|.\sqrt[6]{ y }\\---------------\)
12. \(\dfrac{y^{-1}}{y^{1}}\\= y^{ -1 - 1 }= y^{-2}\\=\frac{1}{y^{2}}\\---------------\)