Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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