Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{1}{3}}}\\= a^{ \frac{1}{2} - \frac{1}{3} }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)
2. \(\dfrac{x^{\frac{5}{3}}}{x^{\frac{-4}{5}}}\\= x^{ \frac{5}{3} - (\frac{-4}{5}) }= x^{\frac{37}{15}}\\=\sqrt[15]{ x^{37} }=x^{2}.\sqrt[15]{ x^{7} }\\---------------\)
3. \(\dfrac{a^{\frac{2}{5}}}{a^{\frac{5}{4}}}\\= a^{ \frac{2}{5} - \frac{5}{4} }= a^{\frac{-17}{20}}\\=\frac{1}{\sqrt[20]{ a^{17} }}=\frac{1}{\sqrt[20]{ a^{17} }}. \color{purple}{\frac{\sqrt[20]{ a^{3} }}{\sqrt[20]{ a^{3} }}} \\=\frac{\sqrt[20]{ a^{3} }}{|a|}\\---------------\)
4. \(\dfrac{q^{\frac{-2}{5}}}{q^{\frac{1}{2}}}\\= q^{ \frac{-2}{5} - \frac{1}{2} }= q^{\frac{-9}{10}}\\=\frac{1}{\sqrt[10]{ q^{9} }}=\frac{1}{\sqrt[10]{ q^{9} }}. \color{purple}{\frac{\sqrt[10]{ q }}{\sqrt[10]{ q }}} \\=\frac{\sqrt[10]{ q }}{|q|}\\---------------\)
5. \(\dfrac{y^{\frac{-1}{6}}}{y^{\frac{-2}{5}}}\\= y^{ \frac{-1}{6} - (\frac{-2}{5}) }= y^{\frac{7}{30}}\\=\sqrt[30]{ y^{7} }\\---------------\)
6. \(\dfrac{y^{\frac{3}{2}}}{y^{2}}\\= y^{ \frac{3}{2} - 2 }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
7. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{-5}{6}}}\\= x^{ \frac{-1}{2} - (\frac{-5}{6}) }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
8. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{4}{5}}}\\= y^{ \frac{2}{3} - \frac{4}{5} }= y^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ y^{2} }}=\frac{1}{\sqrt[15]{ y^{2} }}. \color{purple}{\frac{\sqrt[15]{ y^{13} }}{\sqrt[15]{ y^{13} }}} \\=\frac{\sqrt[15]{ y^{13} }}{y}\\---------------\)
9. \(\dfrac{x^{\frac{-2}{5}}}{x^{\frac{-3}{4}}}\\= x^{ \frac{-2}{5} - (\frac{-3}{4}) }= x^{\frac{7}{20}}\\=\sqrt[20]{ x^{7} }\\---------------\)
10. \(\dfrac{y^{\frac{-4}{3}}}{y^{1}}\\= y^{ \frac{-4}{3} - 1 }= y^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ y^{7} }}\\=\frac{1}{y^{2}.\sqrt[3]{ y }}=\frac{1}{y^{2}.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{3}}\\---------------\)
11. \(\dfrac{a^{\frac{3}{4}}}{a^{\frac{2}{3}}}\\= a^{ \frac{3}{4} - \frac{2}{3} }= a^{\frac{1}{12}}\\=\sqrt[12]{ a }\\---------------\)
12. \(\dfrac{y^{\frac{5}{4}}}{y^{\frac{4}{5}}}\\= y^{ \frac{5}{4} - \frac{4}{5} }= y^{\frac{9}{20}}\\=\sqrt[20]{ y^{9} }\\---------------\)