Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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