Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-3}{4}}}{y^{-1}}\\= y^{ \frac{-3}{4} - (-1) }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)
2. \(\dfrac{q^{\frac{-5}{6}}}{q^{\frac{2}{3}}}\\= q^{ \frac{-5}{6} - \frac{2}{3} }= q^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ q^{3} } }\\=\frac{1}{|q|. \sqrt{ q } }=\frac{1}{|q|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{2}|}\\---------------\)
3. \(\dfrac{y^{\frac{-5}{6}}}{y^{\frac{1}{3}}}\\= y^{ \frac{-5}{6} - \frac{1}{3} }= y^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[6]{ y }}=\frac{1}{|y|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{2}|}\\---------------\)
4. \(\dfrac{q^{\frac{-3}{2}}}{q^{\frac{3}{4}}}\\= q^{ \frac{-3}{2} - \frac{3}{4} }= q^{\frac{-9}{4}}\\=\frac{1}{\sqrt[4]{ q^{9} }}\\=\frac{1}{|q^{2}|.\sqrt[4]{ q }}=\frac{1}{|q^{2}|.\sqrt[4]{ q }} \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q^{3}|}\\---------------\)
5. \(\dfrac{q^{\frac{-4}{3}}}{q^{\frac{1}{3}}}\\= q^{ \frac{-4}{3} - \frac{1}{3} }= q^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ q^{5} }}\\=\frac{1}{q.\sqrt[3]{ q^{2} }}=\frac{1}{q.\sqrt[3]{ q^{2} }} \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{2}}\\---------------\)
6. \(\dfrac{x^{-1}}{x^{\frac{-1}{4}}}\\= x^{ -1 - (\frac{-1}{4}) }= x^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ x^{3} }}=\frac{1}{\sqrt[4]{ x^{3} }}. \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x|}\\---------------\)
7. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{-5}{2}}}\\= a^{ \frac{-1}{3} - (\frac{-5}{2}) }= a^{\frac{13}{6}}\\=\sqrt[6]{ a^{13} }=|a^{2}|.\sqrt[6]{ a }\\---------------\)
8. \(\dfrac{y^{1}}{y^{\frac{3}{5}}}\\= y^{ 1 - \frac{3}{5} }= y^{\frac{2}{5}}\\=\sqrt[5]{ y^{2} }\\---------------\)
9. \(\dfrac{a^{\frac{3}{4}}}{a^{\frac{-5}{6}}}\\= a^{ \frac{3}{4} - (\frac{-5}{6}) }= a^{\frac{19}{12}}\\=\sqrt[12]{ a^{19} }=|a|.\sqrt[12]{ a^{7} }\\---------------\)
10. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{1}{2}}}\\= q^{ \frac{-1}{2} - \frac{1}{2} }= q^{-1}\\=\frac{1}{q}\\---------------\)
11. \(\dfrac{q^{1}}{q^{1}}\\= q^{ 1 - 1 }= q^{0}\\=1\\---------------\)
12. \(\dfrac{q^{1}}{q^{\frac{4}{5}}}\\= q^{ 1 - \frac{4}{5} }= q^{\frac{1}{5}}\\=\sqrt[5]{ q }\\---------------\)