Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{-1}}{y^{\frac{2}{5}}}\\= y^{ -1 - \frac{2}{5} }= y^{\frac{-7}{5}}\\=\frac{1}{\sqrt[5]{ y^{7} }}\\=\frac{1}{y.\sqrt[5]{ y^{2} }}=\frac{1}{y.\sqrt[5]{ y^{2} }} \color{purple}{\frac{\sqrt[5]{ y^{3} }}{\sqrt[5]{ y^{3} }}} \\=\frac{\sqrt[5]{ y^{3} }}{y^{2}}\\---------------\)
2. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{2}{3}}}\\= q^{ \frac{2}{3} - \frac{2}{3} }= q^{0}\\=1\\---------------\)
3. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{-2}{5}}}\\= q^{ \frac{-1}{2} - (\frac{-2}{5}) }= q^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ q }}=\frac{1}{\sqrt[10]{ q }}. \color{purple}{\frac{\sqrt[10]{ q^{9} }}{\sqrt[10]{ q^{9} }}} \\=\frac{\sqrt[10]{ q^{9} }}{|q|}\\---------------\)
4. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{1}{4}}}\\= a^{ \frac{1}{2} - \frac{1}{4} }= a^{\frac{1}{4}}\\=\sqrt[4]{ a }\\---------------\)
5. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{2}{5}}}\\= y^{ \frac{2}{3} - \frac{2}{5} }= y^{\frac{4}{15}}\\=\sqrt[15]{ y^{4} }\\---------------\)
6. \(\dfrac{x^{\frac{2}{5}}}{x^{\frac{4}{5}}}\\= x^{ \frac{2}{5} - \frac{4}{5} }= x^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ x^{2} }}=\frac{1}{\sqrt[5]{ x^{2} }}. \color{purple}{\frac{\sqrt[5]{ x^{3} }}{\sqrt[5]{ x^{3} }}} \\=\frac{\sqrt[5]{ x^{3} }}{x}\\---------------\)
7. \(\dfrac{y^{\frac{-3}{2}}}{y^{\frac{1}{3}}}\\= y^{ \frac{-3}{2} - \frac{1}{3} }= y^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ y^{11} }}\\=\frac{1}{|y|.\sqrt[6]{ y^{5} }}=\frac{1}{|y|.\sqrt[6]{ y^{5} }} \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y^{2}|}\\---------------\)
8. \(\dfrac{y^{\frac{-5}{2}}}{y^{\frac{-5}{6}}}\\= y^{ \frac{-5}{2} - (\frac{-5}{6}) }= y^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ y^{5} }}\\=\frac{1}{y.\sqrt[3]{ y^{2} }}=\frac{1}{y.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{2}}\\---------------\)
9. \(\dfrac{a^{\frac{-1}{5}}}{a^{\frac{5}{6}}}\\= a^{ \frac{-1}{5} - \frac{5}{6} }= a^{\frac{-31}{30}}\\=\frac{1}{\sqrt[30]{ a^{31} }}\\=\frac{1}{|a|.\sqrt[30]{ a }}=\frac{1}{|a|.\sqrt[30]{ a }} \color{purple}{\frac{\sqrt[30]{ a^{29} }}{\sqrt[30]{ a^{29} }}} \\=\frac{\sqrt[30]{ a^{29} }}{|a^{2}|}\\---------------\)
10. \(\dfrac{y^{\frac{1}{4}}}{y^{\frac{3}{5}}}\\= y^{ \frac{1}{4} - \frac{3}{5} }= y^{\frac{-7}{20}}\\=\frac{1}{\sqrt[20]{ y^{7} }}=\frac{1}{\sqrt[20]{ y^{7} }}. \color{purple}{\frac{\sqrt[20]{ y^{13} }}{\sqrt[20]{ y^{13} }}} \\=\frac{\sqrt[20]{ y^{13} }}{|y|}\\---------------\)
11. \(\dfrac{y^{\frac{5}{2}}}{y^{\frac{1}{2}}}\\= y^{ \frac{5}{2} - \frac{1}{2} }= y^{2}\\\\---------------\)
12. \(\dfrac{q^{1}}{q^{1}}\\= q^{ 1 - 1 }= q^{0}\\=1\\---------------\)