Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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