Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-1}{4}}}{a^{\frac{4}{3}}}\\= a^{ \frac{-1}{4} - \frac{4}{3} }= a^{\frac{-19}{12}}\\=\frac{1}{\sqrt[12]{ a^{19} }}\\=\frac{1}{|a|.\sqrt[12]{ a^{7} }}=\frac{1}{|a|.\sqrt[12]{ a^{7} }} \color{purple}{\frac{\sqrt[12]{ a^{5} }}{\sqrt[12]{ a^{5} }}} \\=\frac{\sqrt[12]{ a^{5} }}{|a^{2}|}\\---------------\)
2. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{1}{2} - (\frac{-1}{2}) }= y^{1}\\\\---------------\)
3. \(\dfrac{a^{-1}}{a^{1}}\\= a^{ -1 - 1 }= a^{-2}\\=\frac{1}{a^{2}}\\---------------\)
4. \(\dfrac{a^{1}}{a^{\frac{4}{5}}}\\= a^{ 1 - \frac{4}{5} }= a^{\frac{1}{5}}\\=\sqrt[5]{ a }\\---------------\)
5. \(\dfrac{q^{\frac{1}{5}}}{q^{1}}\\= q^{ \frac{1}{5} - 1 }= q^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ q^{4} }}=\frac{1}{\sqrt[5]{ q^{4} }}. \color{purple}{\frac{\sqrt[5]{ q }}{\sqrt[5]{ q }}} \\=\frac{\sqrt[5]{ q }}{q}\\---------------\)
6. \(\dfrac{q^{-1}}{q^{\frac{1}{5}}}\\= q^{ -1 - \frac{1}{5} }= q^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ q^{6} }}\\=\frac{1}{q.\sqrt[5]{ q }}=\frac{1}{q.\sqrt[5]{ q }} \color{purple}{\frac{\sqrt[5]{ q^{4} }}{\sqrt[5]{ q^{4} }}} \\=\frac{\sqrt[5]{ q^{4} }}{q^{2}}\\---------------\)
7. \(\dfrac{y^{\frac{5}{4}}}{y^{\frac{5}{4}}}\\= y^{ \frac{5}{4} - \frac{5}{4} }= y^{0}\\=1\\---------------\)
8. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{-5}{2}}}\\= y^{ \frac{-1}{3} - (\frac{-5}{2}) }= y^{\frac{13}{6}}\\=\sqrt[6]{ y^{13} }=|y^{2}|.\sqrt[6]{ y }\\---------------\)
9. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{-5}{4}}}\\= q^{ \frac{-1}{3} - (\frac{-5}{4}) }= q^{\frac{11}{12}}\\=\sqrt[12]{ q^{11} }\\---------------\)
10. \(\dfrac{a^{1}}{a^{\frac{5}{6}}}\\= a^{ 1 - \frac{5}{6} }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)
11. \(\dfrac{y^{\frac{5}{2}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{5}{2} - (\frac{-1}{3}) }= y^{\frac{17}{6}}\\=\sqrt[6]{ y^{17} }=|y^{2}|.\sqrt[6]{ y^{5} }\\---------------\)
12. \(\dfrac{q^{\frac{5}{2}}}{q^{\frac{-4}{3}}}\\= q^{ \frac{5}{2} - (\frac{-4}{3}) }= q^{\frac{23}{6}}\\=\sqrt[6]{ q^{23} }=|q^{3}|.\sqrt[6]{ q^{5} }\\---------------\)