Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{1}{2}}}{y^{-1}}\\= y^{ \frac{1}{2} - (-1) }= y^{\frac{3}{2}}\\= \sqrt{ y^{3} } =|y|. \sqrt{ y } \\---------------\)
2. \(\dfrac{q^{\frac{4}{5}}}{q^{\frac{-1}{4}}}\\= q^{ \frac{4}{5} - (\frac{-1}{4}) }= q^{\frac{21}{20}}\\=\sqrt[20]{ q^{21} }=|q|.\sqrt[20]{ q }\\---------------\)
3. \(\dfrac{y^{\frac{-1}{6}}}{y^{\frac{3}{4}}}\\= y^{ \frac{-1}{6} - \frac{3}{4} }= y^{\frac{-11}{12}}\\=\frac{1}{\sqrt[12]{ y^{11} }}=\frac{1}{\sqrt[12]{ y^{11} }}. \color{purple}{\frac{\sqrt[12]{ y }}{\sqrt[12]{ y }}} \\=\frac{\sqrt[12]{ y }}{|y|}\\---------------\)
4. \(\dfrac{x^{\frac{3}{2}}}{x^{\frac{-2}{5}}}\\= x^{ \frac{3}{2} - (\frac{-2}{5}) }= x^{\frac{19}{10}}\\=\sqrt[10]{ x^{19} }=|x|.\sqrt[10]{ x^{9} }\\---------------\)
5. \(\dfrac{x^{\frac{-4}{3}}}{x^{1}}\\= x^{ \frac{-4}{3} - 1 }= x^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ x^{7} }}\\=\frac{1}{x^{2}.\sqrt[3]{ x }}=\frac{1}{x^{2}.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{3}}\\---------------\)
6. \(\dfrac{a^{\frac{-4}{5}}}{a^{1}}\\= a^{ \frac{-4}{5} - 1 }= a^{\frac{-9}{5}}\\=\frac{1}{\sqrt[5]{ a^{9} }}\\=\frac{1}{a.\sqrt[5]{ a^{4} }}=\frac{1}{a.\sqrt[5]{ a^{4} }} \color{purple}{\frac{\sqrt[5]{ a }}{\sqrt[5]{ a }}} \\=\frac{\sqrt[5]{ a }}{a^{2}}\\---------------\)
7. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{1}{2} - (\frac{-1}{3}) }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
8. \(\dfrac{a^{-1}}{a^{-2}}\\= a^{ -1 - (-2) }= a^{1}\\\\---------------\)
9. \(\dfrac{q^{\frac{1}{6}}}{q^{1}}\\= q^{ \frac{1}{6} - 1 }= q^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ q^{5} }}=\frac{1}{\sqrt[6]{ q^{5} }}. \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q|}\\---------------\)
10. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{-5}{6}}}\\= q^{ \frac{1}{3} - (\frac{-5}{6}) }= q^{\frac{7}{6}}\\=\sqrt[6]{ q^{7} }=|q|.\sqrt[6]{ q }\\---------------\)
11. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{-2}{5}}}\\= a^{ \frac{-1}{3} - (\frac{-2}{5}) }= a^{\frac{1}{15}}\\=\sqrt[15]{ a }\\---------------\)
12. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{5}{2}}}\\= x^{ \frac{-1}{2} - \frac{5}{2} }= x^{-3}\\=\frac{1}{x^{3}}\\---------------\)