Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{3}{5}}}{y^{\frac{-5}{2}}}\\= y^{ \frac{3}{5} - (\frac{-5}{2}) }= y^{\frac{31}{10}}\\=\sqrt[10]{ y^{31} }=|y^{3}|.\sqrt[10]{ y }\\---------------\)
2. \(\dfrac{y^{\frac{-1}{6}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{-1}{6} - (\frac{-1}{2}) }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
3. \(\dfrac{x^{\frac{1}{2}}}{x^{1}}\\= x^{ \frac{1}{2} - 1 }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
4. \(\dfrac{q^{\frac{-5}{3}}}{q^{\frac{-5}{6}}}\\= q^{ \frac{-5}{3} - (\frac{-5}{6}) }= q^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ q^{5} }}=\frac{1}{\sqrt[6]{ q^{5} }}. \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q|}\\---------------\)
5. \(\dfrac{a^{\frac{-2}{5}}}{a^{\frac{1}{3}}}\\= a^{ \frac{-2}{5} - \frac{1}{3} }= a^{\frac{-11}{15}}\\=\frac{1}{\sqrt[15]{ a^{11} }}=\frac{1}{\sqrt[15]{ a^{11} }}. \color{purple}{\frac{\sqrt[15]{ a^{4} }}{\sqrt[15]{ a^{4} }}} \\=\frac{\sqrt[15]{ a^{4} }}{a}\\---------------\)
6. \(\dfrac{y^{\frac{-3}{4}}}{y^{1}}\\= y^{ \frac{-3}{4} - 1 }= y^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[4]{ y^{3} }}=\frac{1}{|y|.\sqrt[4]{ y^{3} }} \color{purple}{\frac{\sqrt[4]{ y }}{\sqrt[4]{ y }}} \\=\frac{\sqrt[4]{ y }}{|y^{2}|}\\---------------\)
7. \(\dfrac{y^{\frac{1}{3}}}{y^{-2}}\\= y^{ \frac{1}{3} - (-2) }= y^{\frac{7}{3}}\\=\sqrt[3]{ y^{7} }=y^{2}.\sqrt[3]{ y }\\---------------\)
8. \(\dfrac{q^{1}}{q^{\frac{1}{2}}}\\= q^{ 1 - \frac{1}{2} }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
9. \(\dfrac{y^{\frac{-1}{5}}}{y^{\frac{-1}{4}}}\\= y^{ \frac{-1}{5} - (\frac{-1}{4}) }= y^{\frac{1}{20}}\\=\sqrt[20]{ y }\\---------------\)
10. \(\dfrac{y^{\frac{5}{3}}}{y^{\frac{-5}{6}}}\\= y^{ \frac{5}{3} - (\frac{-5}{6}) }= y^{\frac{5}{2}}\\= \sqrt{ y^{5} } =|y^{2}|. \sqrt{ y } \\---------------\)
11. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{4}{5}}}\\= x^{ \frac{-1}{3} - \frac{4}{5} }= x^{\frac{-17}{15}}\\=\frac{1}{\sqrt[15]{ x^{17} }}\\=\frac{1}{x.\sqrt[15]{ x^{2} }}=\frac{1}{x.\sqrt[15]{ x^{2} }} \color{purple}{\frac{\sqrt[15]{ x^{13} }}{\sqrt[15]{ x^{13} }}} \\=\frac{\sqrt[15]{ x^{13} }}{x^{2}}\\---------------\)
12. \(\dfrac{y^{\frac{-1}{2}}}{y^{-1}}\\= y^{ \frac{-1}{2} - (-1) }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)