Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{3}{5}}}{q^{-1}}\\= q^{ \frac{3}{5} - (-1) }= q^{\frac{8}{5}}\\=\sqrt[5]{ q^{8} }=q.\sqrt[5]{ q^{3} }\\---------------\)
2. \(\dfrac{q^{-1}}{q^{1}}\\= q^{ -1 - 1 }= q^{-2}\\=\frac{1}{q^{2}}\\---------------\)
3. \(\dfrac{q^{\frac{5}{6}}}{q^{-1}}\\= q^{ \frac{5}{6} - (-1) }= q^{\frac{11}{6}}\\=\sqrt[6]{ q^{11} }=|q|.\sqrt[6]{ q^{5} }\\---------------\)
4. \(\dfrac{q^{1}}{q^{\frac{3}{4}}}\\= q^{ 1 - \frac{3}{4} }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
5. \(\dfrac{q^{\frac{1}{4}}}{q^{\frac{1}{3}}}\\= q^{ \frac{1}{4} - \frac{1}{3} }= q^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ q }}=\frac{1}{\sqrt[12]{ q }}. \color{purple}{\frac{\sqrt[12]{ q^{11} }}{\sqrt[12]{ q^{11} }}} \\=\frac{\sqrt[12]{ q^{11} }}{|q|}\\---------------\)
6. \(\dfrac{y^{\frac{1}{3}}}{y^{\frac{1}{4}}}\\= y^{ \frac{1}{3} - \frac{1}{4} }= y^{\frac{1}{12}}\\=\sqrt[12]{ y }\\---------------\)
7. \(\dfrac{q^{\frac{1}{4}}}{q^{\frac{1}{6}}}\\= q^{ \frac{1}{4} - \frac{1}{6} }= q^{\frac{1}{12}}\\=\sqrt[12]{ q }\\---------------\)
8. \(\dfrac{y^{\frac{-2}{5}}}{y^{\frac{-3}{5}}}\\= y^{ \frac{-2}{5} - (\frac{-3}{5}) }= y^{\frac{1}{5}}\\=\sqrt[5]{ y }\\---------------\)
9. \(\dfrac{a^{\frac{-5}{6}}}{a^{\frac{-1}{5}}}\\= a^{ \frac{-5}{6} - (\frac{-1}{5}) }= a^{\frac{-19}{30}}\\=\frac{1}{\sqrt[30]{ a^{19} }}=\frac{1}{\sqrt[30]{ a^{19} }}. \color{purple}{\frac{\sqrt[30]{ a^{11} }}{\sqrt[30]{ a^{11} }}} \\=\frac{\sqrt[30]{ a^{11} }}{|a|}\\---------------\)
10. \(\dfrac{a^{\frac{-3}{4}}}{a^{\frac{2}{3}}}\\= a^{ \frac{-3}{4} - \frac{2}{3} }= a^{\frac{-17}{12}}\\=\frac{1}{\sqrt[12]{ a^{17} }}\\=\frac{1}{|a|.\sqrt[12]{ a^{5} }}=\frac{1}{|a|.\sqrt[12]{ a^{5} }} \color{purple}{\frac{\sqrt[12]{ a^{7} }}{\sqrt[12]{ a^{7} }}} \\=\frac{\sqrt[12]{ a^{7} }}{|a^{2}|}\\---------------\)
11. \(\dfrac{y^{\frac{-3}{5}}}{y^{\frac{-5}{3}}}\\= y^{ \frac{-3}{5} - (\frac{-5}{3}) }= y^{\frac{16}{15}}\\=\sqrt[15]{ y^{16} }=y.\sqrt[15]{ y }\\---------------\)
12. \(\dfrac{a^{\frac{-4}{3}}}{a^{\frac{1}{2}}}\\= a^{ \frac{-4}{3} - \frac{1}{2} }= a^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ a^{11} }}\\=\frac{1}{|a|.\sqrt[6]{ a^{5} }}=\frac{1}{|a|.\sqrt[6]{ a^{5} }} \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a^{2}|}\\---------------\)