Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{1}}{y^{\frac{-2}{3}}}\\= y^{ 1 - (\frac{-2}{3}) }= y^{\frac{5}{3}}\\=\sqrt[3]{ y^{5} }=y.\sqrt[3]{ y^{2} }\\---------------\)
2. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{-2}{5}}}\\= y^{ \frac{1}{2} - (\frac{-2}{5}) }= y^{\frac{9}{10}}\\=\sqrt[10]{ y^{9} }\\---------------\)
3. \(\dfrac{y^{\frac{-2}{3}}}{y^{1}}\\= y^{ \frac{-2}{3} - 1 }= y^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ y^{5} }}\\=\frac{1}{y.\sqrt[3]{ y^{2} }}=\frac{1}{y.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{2}}\\---------------\)
4. \(\dfrac{y^{\frac{5}{3}}}{y^{\frac{3}{5}}}\\= y^{ \frac{5}{3} - \frac{3}{5} }= y^{\frac{16}{15}}\\=\sqrt[15]{ y^{16} }=y.\sqrt[15]{ y }\\---------------\)
5. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{4}{3}}}\\= q^{ \frac{-1}{2} - \frac{4}{3} }= q^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ q^{11} }}\\=\frac{1}{|q|.\sqrt[6]{ q^{5} }}=\frac{1}{|q|.\sqrt[6]{ q^{5} }} \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q^{2}|}\\---------------\)
6. \(\dfrac{q^{\frac{5}{4}}}{q^{\frac{-5}{3}}}\\= q^{ \frac{5}{4} - (\frac{-5}{3}) }= q^{\frac{35}{12}}\\=\sqrt[12]{ q^{35} }=|q^{2}|.\sqrt[12]{ q^{11} }\\---------------\)
7. \(\dfrac{x^{\frac{-4}{5}}}{x^{\frac{5}{4}}}\\= x^{ \frac{-4}{5} - \frac{5}{4} }= x^{\frac{-41}{20}}\\=\frac{1}{\sqrt[20]{ x^{41} }}\\=\frac{1}{|x^{2}|.\sqrt[20]{ x }}=\frac{1}{|x^{2}|.\sqrt[20]{ x }} \color{purple}{\frac{\sqrt[20]{ x^{19} }}{\sqrt[20]{ x^{19} }}} \\=\frac{\sqrt[20]{ x^{19} }}{|x^{3}|}\\---------------\)
8. \(\dfrac{q^{\frac{5}{2}}}{q^{\frac{5}{6}}}\\= q^{ \frac{5}{2} - \frac{5}{6} }= q^{\frac{5}{3}}\\=\sqrt[3]{ q^{5} }=q.\sqrt[3]{ q^{2} }\\---------------\)
9. \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{4}{3}}}\\= x^{ \frac{-2}{3} - \frac{4}{3} }= x^{-2}\\=\frac{1}{x^{2}}\\---------------\)
10. \(\dfrac{x^{-2}}{x^{\frac{1}{2}}}\\= x^{ -2 - \frac{1}{2} }= x^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ x^{5} } }\\=\frac{1}{|x^{2}|. \sqrt{ x } }=\frac{1}{|x^{2}|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{3}|}\\---------------\)
11. \(\dfrac{y^{\frac{-3}{4}}}{y^{\frac{1}{2}}}\\= y^{ \frac{-3}{4} - \frac{1}{2} }= y^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ y^{5} }}\\=\frac{1}{|y|.\sqrt[4]{ y }}=\frac{1}{|y|.\sqrt[4]{ y }} \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y^{2}|}\\---------------\)
12. \(\dfrac{a^{\frac{-5}{6}}}{a^{\frac{1}{5}}}\\= a^{ \frac{-5}{6} - \frac{1}{5} }= a^{\frac{-31}{30}}\\=\frac{1}{\sqrt[30]{ a^{31} }}\\=\frac{1}{|a|.\sqrt[30]{ a }}=\frac{1}{|a|.\sqrt[30]{ a }} \color{purple}{\frac{\sqrt[30]{ a^{29} }}{\sqrt[30]{ a^{29} }}} \\=\frac{\sqrt[30]{ a^{29} }}{|a^{2}|}\\---------------\)