Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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