Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-3}{5}}}{a^{\frac{2}{3}}}\\= a^{ \frac{-3}{5} - \frac{2}{3} }= a^{\frac{-19}{15}}\\=\frac{1}{\sqrt[15]{ a^{19} }}\\=\frac{1}{a.\sqrt[15]{ a^{4} }}=\frac{1}{a.\sqrt[15]{ a^{4} }} \color{purple}{\frac{\sqrt[15]{ a^{11} }}{\sqrt[15]{ a^{11} }}} \\=\frac{\sqrt[15]{ a^{11} }}{a^{2}}\\---------------\)
2. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{-3}{2}}}\\= y^{ \frac{2}{3} - (\frac{-3}{2}) }= y^{\frac{13}{6}}\\=\sqrt[6]{ y^{13} }=|y^{2}|.\sqrt[6]{ y }\\---------------\)
3. \(\dfrac{q^{-2}}{q^{\frac{1}{2}}}\\= q^{ -2 - \frac{1}{2} }= q^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ q^{5} } }\\=\frac{1}{|q^{2}|. \sqrt{ q } }=\frac{1}{|q^{2}|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{3}|}\\---------------\)
4. \(\dfrac{q^{\frac{4}{3}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{4}{3} - (\frac{-1}{3}) }= q^{\frac{5}{3}}\\=\sqrt[3]{ q^{5} }=q.\sqrt[3]{ q^{2} }\\---------------\)
5. \(\dfrac{x^{-2}}{x^{\frac{1}{5}}}\\= x^{ -2 - \frac{1}{5} }= x^{\frac{-11}{5}}\\=\frac{1}{\sqrt[5]{ x^{11} }}\\=\frac{1}{x^{2}.\sqrt[5]{ x }}=\frac{1}{x^{2}.\sqrt[5]{ x }} \color{purple}{\frac{\sqrt[5]{ x^{4} }}{\sqrt[5]{ x^{4} }}} \\=\frac{\sqrt[5]{ x^{4} }}{x^{3}}\\---------------\)
6. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{2}{3}}}\\= q^{ \frac{-1}{2} - \frac{2}{3} }= q^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ q^{7} }}\\=\frac{1}{|q|.\sqrt[6]{ q }}=\frac{1}{|q|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{2}|}\\---------------\)
7. \(\dfrac{y^{\frac{5}{3}}}{y^{\frac{-3}{2}}}\\= y^{ \frac{5}{3} - (\frac{-3}{2}) }= y^{\frac{19}{6}}\\=\sqrt[6]{ y^{19} }=|y^{3}|.\sqrt[6]{ y }\\---------------\)
8. \(\dfrac{q^{\frac{-3}{5}}}{q^{\frac{5}{6}}}\\= q^{ \frac{-3}{5} - \frac{5}{6} }= q^{\frac{-43}{30}}\\=\frac{1}{\sqrt[30]{ q^{43} }}\\=\frac{1}{|q|.\sqrt[30]{ q^{13} }}=\frac{1}{|q|.\sqrt[30]{ q^{13} }} \color{purple}{\frac{\sqrt[30]{ q^{17} }}{\sqrt[30]{ q^{17} }}} \\=\frac{\sqrt[30]{ q^{17} }}{|q^{2}|}\\---------------\)
9. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{1}{4}}}\\= a^{ \frac{2}{3} - \frac{1}{4} }= a^{\frac{5}{12}}\\=\sqrt[12]{ a^{5} }\\---------------\)
10. \(\dfrac{x^{\frac{-1}{4}}}{x^{\frac{-5}{6}}}\\= x^{ \frac{-1}{4} - (\frac{-5}{6}) }= x^{\frac{7}{12}}\\=\sqrt[12]{ x^{7} }\\---------------\)
11. \(\dfrac{x^{\frac{3}{2}}}{x^{\frac{3}{4}}}\\= x^{ \frac{3}{2} - \frac{3}{4} }= x^{\frac{3}{4}}\\=\sqrt[4]{ x^{3} }\\---------------\)
12. \(\dfrac{q^{\frac{-1}{6}}}{q^{\frac{5}{3}}}\\= q^{ \frac{-1}{6} - \frac{5}{3} }= q^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ q^{11} }}\\=\frac{1}{|q|.\sqrt[6]{ q^{5} }}=\frac{1}{|q|.\sqrt[6]{ q^{5} }} \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q^{2}|}\\---------------\)