Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-2}{5}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{-2}{5} - (\frac{-1}{2}) }= x^{\frac{1}{10}}\\=\sqrt[10]{ x }\\---------------\)
2. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{-1}{3} - (\frac{-1}{2}) }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
3. \(\dfrac{x^{\frac{4}{5}}}{x^{\frac{2}{5}}}\\= x^{ \frac{4}{5} - \frac{2}{5} }= x^{\frac{2}{5}}\\=\sqrt[5]{ x^{2} }\\---------------\)
4. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{2}{3} - (\frac{-2}{3}) }= q^{\frac{4}{3}}\\=\sqrt[3]{ q^{4} }=q.\sqrt[3]{ q }\\---------------\)
5. \(\dfrac{x^{\frac{3}{2}}}{x^{\frac{-3}{5}}}\\= x^{ \frac{3}{2} - (\frac{-3}{5}) }= x^{\frac{21}{10}}\\=\sqrt[10]{ x^{21} }=|x^{2}|.\sqrt[10]{ x }\\---------------\)
6. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{1}{3}}}\\= q^{ \frac{-1}{2} - \frac{1}{3} }= q^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ q^{5} }}=\frac{1}{\sqrt[6]{ q^{5} }}. \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q|}\\---------------\)
7. \(\dfrac{a^{-2}}{a^{\frac{-2}{5}}}\\= a^{ -2 - (\frac{-2}{5}) }= a^{\frac{-8}{5}}\\=\frac{1}{\sqrt[5]{ a^{8} }}\\=\frac{1}{a.\sqrt[5]{ a^{3} }}=\frac{1}{a.\sqrt[5]{ a^{3} }} \color{purple}{\frac{\sqrt[5]{ a^{2} }}{\sqrt[5]{ a^{2} }}} \\=\frac{\sqrt[5]{ a^{2} }}{a^{2}}\\---------------\)
8. \(\dfrac{x^{\frac{4}{3}}}{x^{\frac{1}{2}}}\\= x^{ \frac{4}{3} - \frac{1}{2} }= x^{\frac{5}{6}}\\=\sqrt[6]{ x^{5} }\\---------------\)
9. \(\dfrac{a^{\frac{-5}{3}}}{a^{\frac{2}{3}}}\\= a^{ \frac{-5}{3} - \frac{2}{3} }= a^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ a^{7} }}\\=\frac{1}{a^{2}.\sqrt[3]{ a }}=\frac{1}{a^{2}.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{3}}\\---------------\)
10. \(\dfrac{q^{-1}}{q^{\frac{1}{2}}}\\= q^{ -1 - \frac{1}{2} }= q^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ q^{3} } }\\=\frac{1}{|q|. \sqrt{ q } }=\frac{1}{|q|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{2}|}\\---------------\)
11. \(\dfrac{a^{\frac{5}{4}}}{a^{\frac{1}{3}}}\\= a^{ \frac{5}{4} - \frac{1}{3} }= a^{\frac{11}{12}}\\=\sqrt[12]{ a^{11} }\\---------------\)
12. \(\dfrac{y^{\frac{1}{4}}}{y^{\frac{-3}{2}}}\\= y^{ \frac{1}{4} - (\frac{-3}{2}) }= y^{\frac{7}{4}}\\=\sqrt[4]{ y^{7} }=|y|.\sqrt[4]{ y^{3} }\\---------------\)