Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-1}{4}}}{y^{\frac{5}{6}}}\\= y^{ \frac{-1}{4} - \frac{5}{6} }= y^{\frac{-13}{12}}\\=\frac{1}{\sqrt[12]{ y^{13} }}\\=\frac{1}{|y|.\sqrt[12]{ y }}=\frac{1}{|y|.\sqrt[12]{ y }} \color{purple}{\frac{\sqrt[12]{ y^{11} }}{\sqrt[12]{ y^{11} }}} \\=\frac{\sqrt[12]{ y^{11} }}{|y^{2}|}\\---------------\)
2. \(\dfrac{q^{\frac{5}{3}}}{q^{\frac{4}{3}}}\\= q^{ \frac{5}{3} - \frac{4}{3} }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
3. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{-4}{3}}}\\= y^{ \frac{-1}{3} - (\frac{-4}{3}) }= y^{1}\\\\---------------\)
4. \(\dfrac{y^{\frac{-5}{3}}}{y^{\frac{2}{5}}}\\= y^{ \frac{-5}{3} - \frac{2}{5} }= y^{\frac{-31}{15}}\\=\frac{1}{\sqrt[15]{ y^{31} }}\\=\frac{1}{y^{2}.\sqrt[15]{ y }}=\frac{1}{y^{2}.\sqrt[15]{ y }} \color{purple}{\frac{\sqrt[15]{ y^{14} }}{\sqrt[15]{ y^{14} }}} \\=\frac{\sqrt[15]{ y^{14} }}{y^{3}}\\---------------\)
5. \(\dfrac{y^{\frac{5}{2}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{5}{2} - (\frac{-1}{3}) }= y^{\frac{17}{6}}\\=\sqrt[6]{ y^{17} }=|y^{2}|.\sqrt[6]{ y^{5} }\\---------------\)
6. \(\dfrac{y^{\frac{-2}{3}}}{y^{1}}\\= y^{ \frac{-2}{3} - 1 }= y^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ y^{5} }}\\=\frac{1}{y.\sqrt[3]{ y^{2} }}=\frac{1}{y.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{2}}\\---------------\)
7. \(\dfrac{q^{\frac{-2}{5}}}{q^{\frac{1}{5}}}\\= q^{ \frac{-2}{5} - \frac{1}{5} }= q^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ q^{3} }}=\frac{1}{\sqrt[5]{ q^{3} }}. \color{purple}{\frac{\sqrt[5]{ q^{2} }}{\sqrt[5]{ q^{2} }}} \\=\frac{\sqrt[5]{ q^{2} }}{q}\\---------------\)
8. \(\dfrac{x^{-1}}{x^{-1}}\\= x^{ -1 - (-1) }= x^{0}\\=1\\---------------\)
9. \(\dfrac{y^{\frac{-3}{5}}}{y^{\frac{4}{5}}}\\= y^{ \frac{-3}{5} - \frac{4}{5} }= y^{\frac{-7}{5}}\\=\frac{1}{\sqrt[5]{ y^{7} }}\\=\frac{1}{y.\sqrt[5]{ y^{2} }}=\frac{1}{y.\sqrt[5]{ y^{2} }} \color{purple}{\frac{\sqrt[5]{ y^{3} }}{\sqrt[5]{ y^{3} }}} \\=\frac{\sqrt[5]{ y^{3} }}{y^{2}}\\---------------\)
10. \(\dfrac{x^{\frac{1}{6}}}{x^{\frac{-5}{6}}}\\= x^{ \frac{1}{6} - (\frac{-5}{6}) }= x^{1}\\\\---------------\)
11. \(\dfrac{a^{\frac{4}{3}}}{a^{-1}}\\= a^{ \frac{4}{3} - (-1) }= a^{\frac{7}{3}}\\=\sqrt[3]{ a^{7} }=a^{2}.\sqrt[3]{ a }\\---------------\)
12. \(\dfrac{y^{\frac{-3}{2}}}{y^{1}}\\= y^{ \frac{-3}{2} - 1 }= y^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ y^{5} } }\\=\frac{1}{|y^{2}|. \sqrt{ y } }=\frac{1}{|y^{2}|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{3}|}\\---------------\)