Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{4}{5}}}{q^{\frac{2}{3}}}\\= q^{ \frac{4}{5} - \frac{2}{3} }= q^{\frac{2}{15}}\\=\sqrt[15]{ q^{2} }\\---------------\)
2. \(\dfrac{a^{-1}}{a^{2}}\\= a^{ -1 - 2 }= a^{-3}\\=\frac{1}{a^{3}}\\---------------\)
3. \(\dfrac{y^{\frac{-5}{2}}}{y^{\frac{1}{2}}}\\= y^{ \frac{-5}{2} - \frac{1}{2} }= y^{-3}\\=\frac{1}{y^{3}}\\---------------\)
4. \(\dfrac{y^{\frac{1}{3}}}{y^{1}}\\= y^{ \frac{1}{3} - 1 }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
5. \(\dfrac{a^{-1}}{a^{\frac{-5}{3}}}\\= a^{ -1 - (\frac{-5}{3}) }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
6. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{-1}{6}}}\\= q^{ \frac{1}{2} - (\frac{-1}{6}) }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
7. \(\dfrac{q^{\frac{4}{5}}}{q^{\frac{5}{2}}}\\= q^{ \frac{4}{5} - \frac{5}{2} }= q^{\frac{-17}{10}}\\=\frac{1}{\sqrt[10]{ q^{17} }}\\=\frac{1}{|q|.\sqrt[10]{ q^{7} }}=\frac{1}{|q|.\sqrt[10]{ q^{7} }} \color{purple}{\frac{\sqrt[10]{ q^{3} }}{\sqrt[10]{ q^{3} }}} \\=\frac{\sqrt[10]{ q^{3} }}{|q^{2}|}\\---------------\)
8. \(\dfrac{a^{\frac{4}{3}}}{a^{\frac{2}{3}}}\\= a^{ \frac{4}{3} - \frac{2}{3} }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
9. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{2}{3}}}\\= q^{ \frac{-1}{2} - \frac{2}{3} }= q^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ q^{7} }}\\=\frac{1}{|q|.\sqrt[6]{ q }}=\frac{1}{|q|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{2}|}\\---------------\)
10. \(\dfrac{x^{\frac{-1}{5}}}{x^{\frac{3}{4}}}\\= x^{ \frac{-1}{5} - \frac{3}{4} }= x^{\frac{-19}{20}}\\=\frac{1}{\sqrt[20]{ x^{19} }}=\frac{1}{\sqrt[20]{ x^{19} }}. \color{purple}{\frac{\sqrt[20]{ x }}{\sqrt[20]{ x }}} \\=\frac{\sqrt[20]{ x }}{|x|}\\---------------\)
11. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{-4}{3}}}\\= q^{ \frac{-1}{3} - (\frac{-4}{3}) }= q^{1}\\\\---------------\)
12. \(\dfrac{q^{\frac{4}{3}}}{q^{\frac{-4}{3}}}\\= q^{ \frac{4}{3} - (\frac{-4}{3}) }= q^{\frac{8}{3}}\\=\sqrt[3]{ q^{8} }=q^{2}.\sqrt[3]{ q^{2} }\\---------------\)