Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-1}{4}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{-1}{4} - (\frac{-1}{2}) }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)
2. \(\dfrac{y^{\frac{5}{6}}}{y^{\frac{-5}{3}}}\\= y^{ \frac{5}{6} - (\frac{-5}{3}) }= y^{\frac{5}{2}}\\= \sqrt{ y^{5} } =|y^{2}|. \sqrt{ y } \\---------------\)
3. \(\dfrac{x^{-2}}{x^{\frac{1}{3}}}\\= x^{ -2 - \frac{1}{3} }= x^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ x^{7} }}\\=\frac{1}{x^{2}.\sqrt[3]{ x }}=\frac{1}{x^{2}.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{3}}\\---------------\)
4. \(\dfrac{a^{-1}}{a^{\frac{-2}{3}}}\\= a^{ -1 - (\frac{-2}{3}) }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
5. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{-1}{5}}}\\= y^{ \frac{2}{3} - (\frac{-1}{5}) }= y^{\frac{13}{15}}\\=\sqrt[15]{ y^{13} }\\---------------\)
6. \(\dfrac{y^{\frac{-1}{5}}}{y^{\frac{-5}{6}}}\\= y^{ \frac{-1}{5} - (\frac{-5}{6}) }= y^{\frac{19}{30}}\\=\sqrt[30]{ y^{19} }\\---------------\)
7. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{1}{5}}}\\= x^{ \frac{2}{3} - \frac{1}{5} }= x^{\frac{7}{15}}\\=\sqrt[15]{ x^{7} }\\---------------\)
8. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{1}{2} - (\frac{-1}{2}) }= y^{1}\\\\---------------\)
9. \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{1}{3}}}\\= x^{ \frac{-2}{3} - \frac{1}{3} }= x^{-1}\\=\frac{1}{x}\\---------------\)
10. \(\dfrac{a^{-1}}{a^{\frac{-1}{3}}}\\= a^{ -1 - (\frac{-1}{3}) }= a^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ a^{2} }}=\frac{1}{\sqrt[3]{ a^{2} }}. \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a}\\---------------\)
11. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{-1}{3} - (\frac{-1}{2}) }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
12. \(\dfrac{x^{\frac{5}{2}}}{x^{\frac{-4}{5}}}\\= x^{ \frac{5}{2} - (\frac{-4}{5}) }= x^{\frac{33}{10}}\\=\sqrt[10]{ x^{33} }=|x^{3}|.\sqrt[10]{ x^{3} }\\---------------\)