Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{5}{6}}}{q^{\frac{-4}{3}}}\\= q^{ \frac{5}{6} - (\frac{-4}{3}) }= q^{\frac{13}{6}}\\=\sqrt[6]{ q^{13} }=|q^{2}|.\sqrt[6]{ q }\\---------------\)
2. \(\dfrac{y^{1}}{y^{-2}}\\= y^{ 1 - (-2) }= y^{3}\\\\---------------\)
3. \(\dfrac{q^{\frac{-5}{2}}}{q^{1}}\\= q^{ \frac{-5}{2} - 1 }= q^{\frac{-7}{2}}\\=\frac{1}{ \sqrt{ q^{7} } }\\=\frac{1}{|q^{3}|. \sqrt{ q } }=\frac{1}{|q^{3}|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{4}|}\\---------------\)
4. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{-3}{4}}}\\= y^{ \frac{-1}{3} - (\frac{-3}{4}) }= y^{\frac{5}{12}}\\=\sqrt[12]{ y^{5} }\\---------------\)
5. \(\dfrac{y^{\frac{1}{3}}}{y^{-2}}\\= y^{ \frac{1}{3} - (-2) }= y^{\frac{7}{3}}\\=\sqrt[3]{ y^{7} }=y^{2}.\sqrt[3]{ y }\\---------------\)
6. \(\dfrac{y^{-1}}{y^{-1}}\\= y^{ -1 - (-1) }= y^{0}\\=1\\---------------\)
7. \(\dfrac{y^{\frac{5}{4}}}{y^{\frac{-5}{2}}}\\= y^{ \frac{5}{4} - (\frac{-5}{2}) }= y^{\frac{15}{4}}\\=\sqrt[4]{ y^{15} }=|y^{3}|.\sqrt[4]{ y^{3} }\\---------------\)
8. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{-5}{6}}}\\= y^{ \frac{-2}{3} - (\frac{-5}{6}) }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
9. \(\dfrac{a^{\frac{4}{5}}}{a^{-2}}\\= a^{ \frac{4}{5} - (-2) }= a^{\frac{14}{5}}\\=\sqrt[5]{ a^{14} }=a^{2}.\sqrt[5]{ a^{4} }\\---------------\)
10. \(\dfrac{a^{1}}{a^{1}}\\= a^{ 1 - 1 }= a^{0}\\=1\\---------------\)
11. \(\dfrac{a^{\frac{-3}{4}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{-3}{4} - (\frac{-1}{2}) }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
12. \(\dfrac{q^{\frac{-4}{3}}}{q^{2}}\\= q^{ \frac{-4}{3} - 2 }= q^{\frac{-10}{3}}\\=\frac{1}{\sqrt[3]{ q^{10} }}\\=\frac{1}{q^{3}.\sqrt[3]{ q }}=\frac{1}{q^{3}.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{4}}\\---------------\)