Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-5}{4}}}{y^{\frac{-1}{6}}}\\= y^{ \frac{-5}{4} - (\frac{-1}{6}) }= y^{\frac{-13}{12}}\\=\frac{1}{\sqrt[12]{ y^{13} }}\\=\frac{1}{|y|.\sqrt[12]{ y }}=\frac{1}{|y|.\sqrt[12]{ y }} \color{purple}{\frac{\sqrt[12]{ y^{11} }}{\sqrt[12]{ y^{11} }}} \\=\frac{\sqrt[12]{ y^{11} }}{|y^{2}|}\\---------------\)
2. \(\dfrac{a^{\frac{4}{3}}}{a^{-1}}\\= a^{ \frac{4}{3} - (-1) }= a^{\frac{7}{3}}\\=\sqrt[3]{ a^{7} }=a^{2}.\sqrt[3]{ a }\\---------------\)
3. \(\dfrac{q^{-1}}{q^{\frac{2}{3}}}\\= q^{ -1 - \frac{2}{3} }= q^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ q^{5} }}\\=\frac{1}{q.\sqrt[3]{ q^{2} }}=\frac{1}{q.\sqrt[3]{ q^{2} }} \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{2}}\\---------------\)
4. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{5}{4}}}\\= a^{ \frac{-1}{3} - \frac{5}{4} }= a^{\frac{-19}{12}}\\=\frac{1}{\sqrt[12]{ a^{19} }}\\=\frac{1}{|a|.\sqrt[12]{ a^{7} }}=\frac{1}{|a|.\sqrt[12]{ a^{7} }} \color{purple}{\frac{\sqrt[12]{ a^{5} }}{\sqrt[12]{ a^{5} }}} \\=\frac{\sqrt[12]{ a^{5} }}{|a^{2}|}\\---------------\)
5. \(\dfrac{q^{\frac{2}{5}}}{q^{\frac{-3}{4}}}\\= q^{ \frac{2}{5} - (\frac{-3}{4}) }= q^{\frac{23}{20}}\\=\sqrt[20]{ q^{23} }=|q|.\sqrt[20]{ q^{3} }\\---------------\)
6. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{-2}{5}}}\\= q^{ \frac{1}{2} - (\frac{-2}{5}) }= q^{\frac{9}{10}}\\=\sqrt[10]{ q^{9} }\\---------------\)
7. \(\dfrac{y^{\frac{5}{6}}}{y^{\frac{3}{5}}}\\= y^{ \frac{5}{6} - \frac{3}{5} }= y^{\frac{7}{30}}\\=\sqrt[30]{ y^{7} }\\---------------\)
8. \(\dfrac{y^{\frac{-2}{5}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{-2}{5} - (\frac{-1}{2}) }= y^{\frac{1}{10}}\\=\sqrt[10]{ y }\\---------------\)
9. \(\dfrac{q^{-1}}{q^{1}}\\= q^{ -1 - 1 }= q^{-2}\\=\frac{1}{q^{2}}\\---------------\)
10. \(\dfrac{q^{\frac{4}{3}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{4}{3} - (\frac{-1}{2}) }= q^{\frac{11}{6}}\\=\sqrt[6]{ q^{11} }=|q|.\sqrt[6]{ q^{5} }\\---------------\)
11. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{1}{3} - (\frac{-1}{2}) }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
12. \(\dfrac{y^{1}}{y^{-1}}\\= y^{ 1 - (-1) }= y^{2}\\\\---------------\)