Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{-3}{4}}}\\= a^{ \frac{-2}{3} - (\frac{-3}{4}) }= a^{\frac{1}{12}}\\=\sqrt[12]{ a }\\---------------\)
2. \(\dfrac{x^{1}}{x^{\frac{-1}{2}}}\\= x^{ 1 - (\frac{-1}{2}) }= x^{\frac{3}{2}}\\= \sqrt{ x^{3} } =|x|. \sqrt{ x } \\---------------\)
3. \(\dfrac{x^{\frac{-4}{3}}}{x^{\frac{-1}{4}}}\\= x^{ \frac{-4}{3} - (\frac{-1}{4}) }= x^{\frac{-13}{12}}\\=\frac{1}{\sqrt[12]{ x^{13} }}\\=\frac{1}{|x|.\sqrt[12]{ x }}=\frac{1}{|x|.\sqrt[12]{ x }} \color{purple}{\frac{\sqrt[12]{ x^{11} }}{\sqrt[12]{ x^{11} }}} \\=\frac{\sqrt[12]{ x^{11} }}{|x^{2}|}\\---------------\)
4. \(\dfrac{y^{\frac{-1}{5}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{-1}{5} - (\frac{-1}{2}) }= y^{\frac{3}{10}}\\=\sqrt[10]{ y^{3} }\\---------------\)
5. \(\dfrac{x^{-1}}{x^{\frac{-4}{5}}}\\= x^{ -1 - (\frac{-4}{5}) }= x^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ x }}=\frac{1}{\sqrt[5]{ x }}. \color{purple}{\frac{\sqrt[5]{ x^{4} }}{\sqrt[5]{ x^{4} }}} \\=\frac{\sqrt[5]{ x^{4} }}{x}\\---------------\)
6. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{1}{5}}}\\= q^{ \frac{-1}{2} - \frac{1}{5} }= q^{\frac{-7}{10}}\\=\frac{1}{\sqrt[10]{ q^{7} }}=\frac{1}{\sqrt[10]{ q^{7} }}. \color{purple}{\frac{\sqrt[10]{ q^{3} }}{\sqrt[10]{ q^{3} }}} \\=\frac{\sqrt[10]{ q^{3} }}{|q|}\\---------------\)
7. \(\dfrac{y^{1}}{y^{\frac{-4}{5}}}\\= y^{ 1 - (\frac{-4}{5}) }= y^{\frac{9}{5}}\\=\sqrt[5]{ y^{9} }=y.\sqrt[5]{ y^{4} }\\---------------\)
8. \(\dfrac{y^{\frac{-1}{6}}}{y^{\frac{-1}{6}}}\\= y^{ \frac{-1}{6} - (\frac{-1}{6}) }= y^{0}\\=1\\---------------\)
9. \(\dfrac{q^{\frac{-3}{2}}}{q^{\frac{1}{2}}}\\= q^{ \frac{-3}{2} - \frac{1}{2} }= q^{-2}\\=\frac{1}{q^{2}}\\---------------\)
10. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{1}{5}}}\\= q^{ \frac{-2}{3} - \frac{1}{5} }= q^{\frac{-13}{15}}\\=\frac{1}{\sqrt[15]{ q^{13} }}=\frac{1}{\sqrt[15]{ q^{13} }}. \color{purple}{\frac{\sqrt[15]{ q^{2} }}{\sqrt[15]{ q^{2} }}} \\=\frac{\sqrt[15]{ q^{2} }}{q}\\---------------\)
11. \(\dfrac{a^{\frac{-5}{2}}}{a^{-1}}\\= a^{ \frac{-5}{2} - (-1) }= a^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ a^{3} } }\\=\frac{1}{|a|. \sqrt{ a } }=\frac{1}{|a|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{2}|}\\---------------\)
12. \(\dfrac{x^{\frac{3}{2}}}{x^{\frac{-4}{3}}}\\= x^{ \frac{3}{2} - (\frac{-4}{3}) }= x^{\frac{17}{6}}\\=\sqrt[6]{ x^{17} }=|x^{2}|.\sqrt[6]{ x^{5} }\\---------------\)