Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{-1}}{q^{-2}}\\= q^{ -1 - (-2) }= q^{1}\\\\---------------\)
2. \(\dfrac{a^{\frac{3}{5}}}{a^{\frac{3}{4}}}\\= a^{ \frac{3}{5} - \frac{3}{4} }= a^{\frac{-3}{20}}\\=\frac{1}{\sqrt[20]{ a^{3} }}=\frac{1}{\sqrt[20]{ a^{3} }}. \color{purple}{\frac{\sqrt[20]{ a^{17} }}{\sqrt[20]{ a^{17} }}} \\=\frac{\sqrt[20]{ a^{17} }}{|a|}\\---------------\)
3. \(\dfrac{q^{-1}}{q^{\frac{-1}{3}}}\\= q^{ -1 - (\frac{-1}{3}) }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)
4. \(\dfrac{q^{\frac{-3}{2}}}{q^{\frac{3}{2}}}\\= q^{ \frac{-3}{2} - \frac{3}{2} }= q^{-3}\\=\frac{1}{q^{3}}\\---------------\)
5. \(\dfrac{a^{\frac{-5}{6}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{-5}{6} - (\frac{-1}{3}) }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
6. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{4}{3}}}\\= a^{ \frac{1}{3} - \frac{4}{3} }= a^{-1}\\=\frac{1}{a}\\---------------\)
7. \(\dfrac{a^{\frac{-4}{5}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{-4}{5} - (\frac{-1}{3}) }= a^{\frac{-7}{15}}\\=\frac{1}{\sqrt[15]{ a^{7} }}=\frac{1}{\sqrt[15]{ a^{7} }}. \color{purple}{\frac{\sqrt[15]{ a^{8} }}{\sqrt[15]{ a^{8} }}} \\=\frac{\sqrt[15]{ a^{8} }}{a}\\---------------\)
8. \(\dfrac{x^{\frac{-1}{4}}}{x^{\frac{3}{5}}}\\= x^{ \frac{-1}{4} - \frac{3}{5} }= x^{\frac{-17}{20}}\\=\frac{1}{\sqrt[20]{ x^{17} }}=\frac{1}{\sqrt[20]{ x^{17} }}. \color{purple}{\frac{\sqrt[20]{ x^{3} }}{\sqrt[20]{ x^{3} }}} \\=\frac{\sqrt[20]{ x^{3} }}{|x|}\\---------------\)
9. \(\dfrac{x^{\frac{3}{4}}}{x^{\frac{2}{3}}}\\= x^{ \frac{3}{4} - \frac{2}{3} }= x^{\frac{1}{12}}\\=\sqrt[12]{ x }\\---------------\)
10. \(\dfrac{a^{2}}{a^{\frac{1}{2}}}\\= a^{ 2 - \frac{1}{2} }= a^{\frac{3}{2}}\\= \sqrt{ a^{3} } =|a|. \sqrt{ a } \\---------------\)
11. \(\dfrac{y^{\frac{1}{3}}}{y^{1}}\\= y^{ \frac{1}{3} - 1 }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
12. \(\dfrac{x^{\frac{5}{4}}}{x^{\frac{1}{6}}}\\= x^{ \frac{5}{4} - \frac{1}{6} }= x^{\frac{13}{12}}\\=\sqrt[12]{ x^{13} }=|x|.\sqrt[12]{ x }\\---------------\)