Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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