Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-1}{4}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{-1}{4} - (\frac{-1}{2}) }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
2. \(\dfrac{q^{\frac{-3}{5}}}{q^{\frac{1}{3}}}\\= q^{ \frac{-3}{5} - \frac{1}{3} }= q^{\frac{-14}{15}}\\=\frac{1}{\sqrt[15]{ q^{14} }}=\frac{1}{\sqrt[15]{ q^{14} }}. \color{purple}{\frac{\sqrt[15]{ q }}{\sqrt[15]{ q }}} \\=\frac{\sqrt[15]{ q }}{q}\\---------------\)
3. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{3}{5}}}\\= a^{ \frac{2}{3} - \frac{3}{5} }= a^{\frac{1}{15}}\\=\sqrt[15]{ a }\\---------------\)
4. \(\dfrac{y^{\frac{1}{3}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{1}{3} - (\frac{-1}{3}) }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
5. \(\dfrac{y^{\frac{4}{3}}}{y^{\frac{2}{3}}}\\= y^{ \frac{4}{3} - \frac{2}{3} }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
6. \(\dfrac{a^{\frac{2}{5}}}{a^{\frac{5}{4}}}\\= a^{ \frac{2}{5} - \frac{5}{4} }= a^{\frac{-17}{20}}\\=\frac{1}{\sqrt[20]{ a^{17} }}=\frac{1}{\sqrt[20]{ a^{17} }}. \color{purple}{\frac{\sqrt[20]{ a^{3} }}{\sqrt[20]{ a^{3} }}} \\=\frac{\sqrt[20]{ a^{3} }}{|a|}\\---------------\)
7. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{1}{2} - (\frac{-1}{2}) }= x^{1}\\\\---------------\)
8. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{5}{4}}}\\= q^{ \frac{1}{2} - \frac{5}{4} }= q^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ q^{3} }}=\frac{1}{\sqrt[4]{ q^{3} }}. \color{purple}{\frac{\sqrt[4]{ q }}{\sqrt[4]{ q }}} \\=\frac{\sqrt[4]{ q }}{|q|}\\---------------\)
9. \(\dfrac{a^{\frac{1}{4}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{1}{4} - (\frac{-2}{3}) }= a^{\frac{11}{12}}\\=\sqrt[12]{ a^{11} }\\---------------\)
10. \(\dfrac{q^{\frac{-1}{6}}}{q^{1}}\\= q^{ \frac{-1}{6} - 1 }= q^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ q^{7} }}\\=\frac{1}{|q|.\sqrt[6]{ q }}=\frac{1}{|q|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{2}|}\\---------------\)
11. \(\dfrac{a^{\frac{4}{3}}}{a^{-2}}\\= a^{ \frac{4}{3} - (-2) }= a^{\frac{10}{3}}\\=\sqrt[3]{ a^{10} }=a^{3}.\sqrt[3]{ a }\\---------------\)
12. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{5}{3}}}\\= y^{ \frac{-2}{3} - \frac{5}{3} }= y^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ y^{7} }}\\=\frac{1}{y^{2}.\sqrt[3]{ y }}=\frac{1}{y^{2}.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{3}}\\---------------\)