Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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