Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{-2}}{a^{-1}}\\= a^{ -2 - (-1) }= a^{-1}\\=\frac{1}{a}\\---------------\)
2. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{1}{5}}}\\= y^{ \frac{1}{2} - \frac{1}{5} }= y^{\frac{3}{10}}\\=\sqrt[10]{ y^{3} }\\---------------\)
3. \(\dfrac{q^{\frac{-3}{2}}}{q^{\frac{-2}{5}}}\\= q^{ \frac{-3}{2} - (\frac{-2}{5}) }= q^{\frac{-11}{10}}\\=\frac{1}{\sqrt[10]{ q^{11} }}\\=\frac{1}{|q|.\sqrt[10]{ q }}=\frac{1}{|q|.\sqrt[10]{ q }} \color{purple}{\frac{\sqrt[10]{ q^{9} }}{\sqrt[10]{ q^{9} }}} \\=\frac{\sqrt[10]{ q^{9} }}{|q^{2}|}\\---------------\)
4. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{-2}{5}}}\\= y^{ \frac{-1}{2} - (\frac{-2}{5}) }= y^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ y }}=\frac{1}{\sqrt[10]{ y }}. \color{purple}{\frac{\sqrt[10]{ y^{9} }}{\sqrt[10]{ y^{9} }}} \\=\frac{\sqrt[10]{ y^{9} }}{|y|}\\---------------\)
5. \(\dfrac{q^{\frac{3}{2}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{3}{2} - (\frac{-2}{3}) }= q^{\frac{13}{6}}\\=\sqrt[6]{ q^{13} }=|q^{2}|.\sqrt[6]{ q }\\---------------\)
6. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{2}{3} - (\frac{-1}{2}) }= q^{\frac{7}{6}}\\=\sqrt[6]{ q^{7} }=|q|.\sqrt[6]{ q }\\---------------\)
7. \(\dfrac{y^{\frac{3}{2}}}{y^{\frac{-1}{6}}}\\= y^{ \frac{3}{2} - (\frac{-1}{6}) }= y^{\frac{5}{3}}\\=\sqrt[3]{ y^{5} }=y.\sqrt[3]{ y^{2} }\\---------------\)
8. \(\dfrac{a^{\frac{-5}{2}}}{a^{-1}}\\= a^{ \frac{-5}{2} - (-1) }= a^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ a^{3} } }\\=\frac{1}{|a|. \sqrt{ a } }=\frac{1}{|a|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{2}|}\\---------------\)
9. \(\dfrac{q^{\frac{-1}{4}}}{q^{\frac{-1}{6}}}\\= q^{ \frac{-1}{4} - (\frac{-1}{6}) }= q^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ q }}=\frac{1}{\sqrt[12]{ q }}. \color{purple}{\frac{\sqrt[12]{ q^{11} }}{\sqrt[12]{ q^{11} }}} \\=\frac{\sqrt[12]{ q^{11} }}{|q|}\\---------------\)
10. \(\dfrac{a^{\frac{5}{3}}}{a^{\frac{3}{5}}}\\= a^{ \frac{5}{3} - \frac{3}{5} }= a^{\frac{16}{15}}\\=\sqrt[15]{ a^{16} }=a.\sqrt[15]{ a }\\---------------\)
11. \(\dfrac{x^{2}}{x^{\frac{-4}{3}}}\\= x^{ 2 - (\frac{-4}{3}) }= x^{\frac{10}{3}}\\=\sqrt[3]{ x^{10} }=x^{3}.\sqrt[3]{ x }\\---------------\)
12. \(\dfrac{x^{1}}{x^{\frac{-4}{5}}}\\= x^{ 1 - (\frac{-4}{5}) }= x^{\frac{9}{5}}\\=\sqrt[5]{ x^{9} }=x.\sqrt[5]{ x^{4} }\\---------------\)