Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{-1}}{a^{\frac{-5}{3}}}\\= a^{ -1 - (\frac{-5}{3}) }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
2. \(\dfrac{a^{-1}}{a^{\frac{-3}{5}}}\\= a^{ -1 - (\frac{-3}{5}) }= a^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ a^{2} }}=\frac{1}{\sqrt[5]{ a^{2} }}. \color{purple}{\frac{\sqrt[5]{ a^{3} }}{\sqrt[5]{ a^{3} }}} \\=\frac{\sqrt[5]{ a^{3} }}{a}\\---------------\)
3. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{2}{3} - (\frac{-2}{3}) }= y^{\frac{4}{3}}\\=\sqrt[3]{ y^{4} }=y.\sqrt[3]{ y }\\---------------\)
4. \(\dfrac{x^{\frac{-1}{6}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{-1}{6} - (\frac{-1}{3}) }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
5. \(\dfrac{q^{\frac{-1}{5}}}{q^{\frac{1}{2}}}\\= q^{ \frac{-1}{5} - \frac{1}{2} }= q^{\frac{-7}{10}}\\=\frac{1}{\sqrt[10]{ q^{7} }}=\frac{1}{\sqrt[10]{ q^{7} }}. \color{purple}{\frac{\sqrt[10]{ q^{3} }}{\sqrt[10]{ q^{3} }}} \\=\frac{\sqrt[10]{ q^{3} }}{|q|}\\---------------\)
6. \(\dfrac{q^{\frac{2}{5}}}{q^{\frac{1}{5}}}\\= q^{ \frac{2}{5} - \frac{1}{5} }= q^{\frac{1}{5}}\\=\sqrt[5]{ q }\\---------------\)
7. \(\dfrac{y^{2}}{y^{\frac{-3}{4}}}\\= y^{ 2 - (\frac{-3}{4}) }= y^{\frac{11}{4}}\\=\sqrt[4]{ y^{11} }=|y^{2}|.\sqrt[4]{ y^{3} }\\---------------\)
8. \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{2}{5}}}\\= x^{ \frac{-2}{3} - \frac{2}{5} }= x^{\frac{-16}{15}}\\=\frac{1}{\sqrt[15]{ x^{16} }}\\=\frac{1}{x.\sqrt[15]{ x }}=\frac{1}{x.\sqrt[15]{ x }} \color{purple}{\frac{\sqrt[15]{ x^{14} }}{\sqrt[15]{ x^{14} }}} \\=\frac{\sqrt[15]{ x^{14} }}{x^{2}}\\---------------\)
9. \(\dfrac{y^{\frac{1}{2}}}{y^{-1}}\\= y^{ \frac{1}{2} - (-1) }= y^{\frac{3}{2}}\\= \sqrt{ y^{3} } =|y|. \sqrt{ y } \\---------------\)
10. \(\dfrac{q^{\frac{3}{2}}}{q^{\frac{-3}{5}}}\\= q^{ \frac{3}{2} - (\frac{-3}{5}) }= q^{\frac{21}{10}}\\=\sqrt[10]{ q^{21} }=|q^{2}|.\sqrt[10]{ q }\\---------------\)
11. \(\dfrac{x^{\frac{5}{2}}}{x^{\frac{2}{5}}}\\= x^{ \frac{5}{2} - \frac{2}{5} }= x^{\frac{21}{10}}\\=\sqrt[10]{ x^{21} }=|x^{2}|.\sqrt[10]{ x }\\---------------\)
12. \(\dfrac{y^{\frac{-1}{6}}}{y^{\frac{3}{5}}}\\= y^{ \frac{-1}{6} - \frac{3}{5} }= y^{\frac{-23}{30}}\\=\frac{1}{\sqrt[30]{ y^{23} }}=\frac{1}{\sqrt[30]{ y^{23} }}. \color{purple}{\frac{\sqrt[30]{ y^{7} }}{\sqrt[30]{ y^{7} }}} \\=\frac{\sqrt[30]{ y^{7} }}{|y|}\\---------------\)