Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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