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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{1}{4}}}{q^{\frac{1}{2}}}\\= q^{ \frac{1}{4} - \frac{1}{2} }= q^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ q }}=\frac{1}{\sqrt[4]{ q }}. \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q|}\\---------------\)
2. \(\dfrac{a^{\frac{3}{5}}}{a^{-1}}\\= a^{ \frac{3}{5} - (-1) }= a^{\frac{8}{5}}\\=\sqrt[5]{ a^{8} }=a.\sqrt[5]{ a^{3} }\\---------------\)
3. \(\dfrac{q^{\frac{-3}{2}}}{q^{\frac{5}{2}}}\\= q^{ \frac{-3}{2} - \frac{5}{2} }= q^{-4}\\=\frac{1}{q^{4}}\\---------------\)
4. \(\dfrac{q^{\frac{4}{3}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{4}{3} - (\frac{-2}{3}) }= q^{2}\\\\---------------\)
5. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{-2}{3} - (\frac{-1}{2}) }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)
6. \(\dfrac{y^{\frac{-5}{3}}}{y^{\frac{3}{4}}}\\= y^{ \frac{-5}{3} - \frac{3}{4} }= y^{\frac{-29}{12}}\\=\frac{1}{\sqrt[12]{ y^{29} }}\\=\frac{1}{|y^{2}|.\sqrt[12]{ y^{5} }}=\frac{1}{|y^{2}|.\sqrt[12]{ y^{5} }} \color{purple}{\frac{\sqrt[12]{ y^{7} }}{\sqrt[12]{ y^{7} }}} \\=\frac{\sqrt[12]{ y^{7} }}{|y^{3}|}\\---------------\)
7. \(\dfrac{q^{\frac{5}{4}}}{q^{\frac{-4}{5}}}\\= q^{ \frac{5}{4} - (\frac{-4}{5}) }= q^{\frac{41}{20}}\\=\sqrt[20]{ q^{41} }=|q^{2}|.\sqrt[20]{ q }\\---------------\)
8. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{1}{2} - (\frac{-1}{3}) }= a^{\frac{5}{6}}\\=\sqrt[6]{ a^{5} }\\---------------\)
9. \(\dfrac{y^{\frac{1}{6}}}{y^{\frac{1}{6}}}\\= y^{ \frac{1}{6} - \frac{1}{6} }= y^{0}\\=1\\---------------\)
10. \(\dfrac{a^{\frac{2}{5}}}{a^{\frac{5}{3}}}\\= a^{ \frac{2}{5} - \frac{5}{3} }= a^{\frac{-19}{15}}\\=\frac{1}{\sqrt[15]{ a^{19} }}\\=\frac{1}{a.\sqrt[15]{ a^{4} }}=\frac{1}{a.\sqrt[15]{ a^{4} }} \color{purple}{\frac{\sqrt[15]{ a^{11} }}{\sqrt[15]{ a^{11} }}} \\=\frac{\sqrt[15]{ a^{11} }}{a^{2}}\\---------------\)
11. \(\dfrac{q^{\frac{5}{4}}}{q^{1}}\\= q^{ \frac{5}{4} - 1 }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
12. \(\dfrac{a^{\frac{3}{5}}}{a^{\frac{5}{3}}}\\= a^{ \frac{3}{5} - \frac{5}{3} }= a^{\frac{-16}{15}}\\=\frac{1}{\sqrt[15]{ a^{16} }}\\=\frac{1}{a.\sqrt[15]{ a }}=\frac{1}{a.\sqrt[15]{ a }} \color{purple}{\frac{\sqrt[15]{ a^{14} }}{\sqrt[15]{ a^{14} }}} \\=\frac{\sqrt[15]{ a^{14} }}{a^{2}}\\---------------\)