Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{1}{3}}}{y^{\frac{1}{5}}}\\= y^{ \frac{1}{3} - \frac{1}{5} }= y^{\frac{2}{15}}\\=\sqrt[15]{ y^{2} }\\---------------\)
2. \(\dfrac{q^{\frac{2}{3}}}{q^{-1}}\\= q^{ \frac{2}{3} - (-1) }= q^{\frac{5}{3}}\\=\sqrt[3]{ q^{5} }=q.\sqrt[3]{ q^{2} }\\---------------\)
3. \(\dfrac{a^{\frac{1}{4}}}{a^{\frac{-2}{5}}}\\= a^{ \frac{1}{4} - (\frac{-2}{5}) }= a^{\frac{13}{20}}\\=\sqrt[20]{ a^{13} }\\---------------\)
4. \(\dfrac{a^{\frac{5}{4}}}{a^{\frac{1}{5}}}\\= a^{ \frac{5}{4} - \frac{1}{5} }= a^{\frac{21}{20}}\\=\sqrt[20]{ a^{21} }=|a|.\sqrt[20]{ a }\\---------------\)
5. \(\dfrac{q^{\frac{-4}{5}}}{q^{-1}}\\= q^{ \frac{-4}{5} - (-1) }= q^{\frac{1}{5}}\\=\sqrt[5]{ q }\\---------------\)
6. \(\dfrac{q^{\frac{4}{3}}}{q^{\frac{-5}{3}}}\\= q^{ \frac{4}{3} - (\frac{-5}{3}) }= q^{3}\\\\---------------\)
7. \(\dfrac{a^{2}}{a^{\frac{-1}{3}}}\\= a^{ 2 - (\frac{-1}{3}) }= a^{\frac{7}{3}}\\=\sqrt[3]{ a^{7} }=a^{2}.\sqrt[3]{ a }\\---------------\)
8. \(\dfrac{a^{\frac{-5}{2}}}{a^{\frac{-3}{5}}}\\= a^{ \frac{-5}{2} - (\frac{-3}{5}) }= a^{\frac{-19}{10}}\\=\frac{1}{\sqrt[10]{ a^{19} }}\\=\frac{1}{|a|.\sqrt[10]{ a^{9} }}=\frac{1}{|a|.\sqrt[10]{ a^{9} }} \color{purple}{\frac{\sqrt[10]{ a }}{\sqrt[10]{ a }}} \\=\frac{\sqrt[10]{ a }}{|a^{2}|}\\---------------\)
9. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{1}{6}}}\\= q^{ \frac{1}{2} - \frac{1}{6} }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
10. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{-5}{2}}}\\= a^{ \frac{1}{2} - (\frac{-5}{2}) }= a^{3}\\\\---------------\)
11. \(\dfrac{a^{\frac{5}{4}}}{a^{\frac{-1}{6}}}\\= a^{ \frac{5}{4} - (\frac{-1}{6}) }= a^{\frac{17}{12}}\\=\sqrt[12]{ a^{17} }=|a|.\sqrt[12]{ a^{5} }\\---------------\)
12. \(\dfrac{x^{1}}{x^{\frac{-2}{3}}}\\= x^{ 1 - (\frac{-2}{3}) }= x^{\frac{5}{3}}\\=\sqrt[3]{ x^{5} }=x.\sqrt[3]{ x^{2} }\\---------------\)