Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-5}{3}}}{a^{\frac{5}{2}}}\\= a^{ \frac{-5}{3} - \frac{5}{2} }= a^{\frac{-25}{6}}\\=\frac{1}{\sqrt[6]{ a^{25} }}\\=\frac{1}{|a^{4}|.\sqrt[6]{ a }}=\frac{1}{|a^{4}|.\sqrt[6]{ a }} \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a^{5}|}\\---------------\)
2. \(\dfrac{y^{\frac{1}{3}}}{y^{\frac{-5}{2}}}\\= y^{ \frac{1}{3} - (\frac{-5}{2}) }= y^{\frac{17}{6}}\\=\sqrt[6]{ y^{17} }=|y^{2}|.\sqrt[6]{ y^{5} }\\---------------\)
3. \(\dfrac{x^{1}}{x^{\frac{1}{2}}}\\= x^{ 1 - \frac{1}{2} }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
4. \(\dfrac{q^{\frac{4}{3}}}{q^{\frac{-2}{5}}}\\= q^{ \frac{4}{3} - (\frac{-2}{5}) }= q^{\frac{26}{15}}\\=\sqrt[15]{ q^{26} }=q.\sqrt[15]{ q^{11} }\\---------------\)
5. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{-1}{2} - (\frac{-2}{3}) }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
6. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{1}{2}}}\\= a^{ \frac{1}{3} - \frac{1}{2} }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
7. \(\dfrac{a^{\frac{-1}{5}}}{a^{\frac{-3}{5}}}\\= a^{ \frac{-1}{5} - (\frac{-3}{5}) }= a^{\frac{2}{5}}\\=\sqrt[5]{ a^{2} }\\---------------\)
8. \(\dfrac{a^{\frac{-5}{3}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{-5}{3} - (\frac{-1}{2}) }= a^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ a^{7} }}\\=\frac{1}{|a|.\sqrt[6]{ a }}=\frac{1}{|a|.\sqrt[6]{ a }} \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a^{2}|}\\---------------\)
9. \(\dfrac{q^{1}}{q^{\frac{-1}{2}}}\\= q^{ 1 - (\frac{-1}{2}) }= q^{\frac{3}{2}}\\= \sqrt{ q^{3} } =|q|. \sqrt{ q } \\---------------\)
10. \(\dfrac{y^{\frac{5}{6}}}{y^{\frac{-3}{5}}}\\= y^{ \frac{5}{6} - (\frac{-3}{5}) }= y^{\frac{43}{30}}\\=\sqrt[30]{ y^{43} }=|y|.\sqrt[30]{ y^{13} }\\---------------\)
11. \(\dfrac{a^{\frac{5}{2}}}{a^{\frac{1}{4}}}\\= a^{ \frac{5}{2} - \frac{1}{4} }= a^{\frac{9}{4}}\\=\sqrt[4]{ a^{9} }=|a^{2}|.\sqrt[4]{ a }\\---------------\)
12. \(\dfrac{y^{-1}}{y^{\frac{5}{6}}}\\= y^{ -1 - \frac{5}{6} }= y^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ y^{11} }}\\=\frac{1}{|y|.\sqrt[6]{ y^{5} }}=\frac{1}{|y|.\sqrt[6]{ y^{5} }} \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y^{2}|}\\---------------\)