Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-1}{5}}}{x^{-1}}\\= x^{ \frac{-1}{5} - (-1) }= x^{\frac{4}{5}}\\=\sqrt[5]{ x^{4} }\\---------------\)
2. \(\dfrac{y^{-1}}{y^{\frac{4}{5}}}\\= y^{ -1 - \frac{4}{5} }= y^{\frac{-9}{5}}\\=\frac{1}{\sqrt[5]{ y^{9} }}\\=\frac{1}{y.\sqrt[5]{ y^{4} }}=\frac{1}{y.\sqrt[5]{ y^{4} }} \color{purple}{\frac{\sqrt[5]{ y }}{\sqrt[5]{ y }}} \\=\frac{\sqrt[5]{ y }}{y^{2}}\\---------------\)
3. \(\dfrac{q^{\frac{-4}{3}}}{q^{\frac{2}{3}}}\\= q^{ \frac{-4}{3} - \frac{2}{3} }= q^{-2}\\=\frac{1}{q^{2}}\\---------------\)
4. \(\dfrac{y^{\frac{-3}{4}}}{y^{\frac{1}{4}}}\\= y^{ \frac{-3}{4} - \frac{1}{4} }= y^{-1}\\=\frac{1}{y}\\---------------\)
5. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{2}{3} - (\frac{-1}{2}) }= y^{\frac{7}{6}}\\=\sqrt[6]{ y^{7} }=|y|.\sqrt[6]{ y }\\---------------\)
6. \(\dfrac{a^{\frac{-4}{5}}}{a^{-2}}\\= a^{ \frac{-4}{5} - (-2) }= a^{\frac{6}{5}}\\=\sqrt[5]{ a^{6} }=a.\sqrt[5]{ a }\\---------------\)
7. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{1}{4}}}\\= y^{ \frac{1}{2} - \frac{1}{4} }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)
8. \(\dfrac{a^{\frac{3}{5}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{3}{5} - (\frac{-2}{3}) }= a^{\frac{19}{15}}\\=\sqrt[15]{ a^{19} }=a.\sqrt[15]{ a^{4} }\\---------------\)
9. \(\dfrac{y^{\frac{3}{4}}}{y^{\frac{3}{4}}}\\= y^{ \frac{3}{4} - \frac{3}{4} }= y^{0}\\=1\\---------------\)
10. \(\dfrac{q^{2}}{q^{\frac{-1}{2}}}\\= q^{ 2 - (\frac{-1}{2}) }= q^{\frac{5}{2}}\\= \sqrt{ q^{5} } =|q^{2}|. \sqrt{ q } \\---------------\)
11. \(\dfrac{q^{\frac{1}{5}}}{q^{\frac{4}{3}}}\\= q^{ \frac{1}{5} - \frac{4}{3} }= q^{\frac{-17}{15}}\\=\frac{1}{\sqrt[15]{ q^{17} }}\\=\frac{1}{q.\sqrt[15]{ q^{2} }}=\frac{1}{q.\sqrt[15]{ q^{2} }} \color{purple}{\frac{\sqrt[15]{ q^{13} }}{\sqrt[15]{ q^{13} }}} \\=\frac{\sqrt[15]{ q^{13} }}{q^{2}}\\---------------\)
12. \(\dfrac{y^{\frac{-4}{5}}}{y^{\frac{1}{3}}}\\= y^{ \frac{-4}{5} - \frac{1}{3} }= y^{\frac{-17}{15}}\\=\frac{1}{\sqrt[15]{ y^{17} }}\\=\frac{1}{y.\sqrt[15]{ y^{2} }}=\frac{1}{y.\sqrt[15]{ y^{2} }} \color{purple}{\frac{\sqrt[15]{ y^{13} }}{\sqrt[15]{ y^{13} }}} \\=\frac{\sqrt[15]{ y^{13} }}{y^{2}}\\---------------\)