Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{-1}}{y^{\frac{-4}{5}}}\\= y^{ -1 - (\frac{-4}{5}) }= y^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ y }}=\frac{1}{\sqrt[5]{ y }}. \color{purple}{\frac{\sqrt[5]{ y^{4} }}{\sqrt[5]{ y^{4} }}} \\=\frac{\sqrt[5]{ y^{4} }}{y}\\---------------\)
2. \(\dfrac{y^{\frac{3}{5}}}{y^{\frac{-1}{6}}}\\= y^{ \frac{3}{5} - (\frac{-1}{6}) }= y^{\frac{23}{30}}\\=\sqrt[30]{ y^{23} }\\---------------\)
3. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{3}{2}}}\\= a^{ \frac{1}{2} - \frac{3}{2} }= a^{-1}\\=\frac{1}{a}\\---------------\)
4. \(\dfrac{q^{\frac{-4}{5}}}{q^{\frac{5}{3}}}\\= q^{ \frac{-4}{5} - \frac{5}{3} }= q^{\frac{-37}{15}}\\=\frac{1}{\sqrt[15]{ q^{37} }}\\=\frac{1}{q^{2}.\sqrt[15]{ q^{7} }}=\frac{1}{q^{2}.\sqrt[15]{ q^{7} }} \color{purple}{\frac{\sqrt[15]{ q^{8} }}{\sqrt[15]{ q^{8} }}} \\=\frac{\sqrt[15]{ q^{8} }}{q^{3}}\\---------------\)
5. \(\dfrac{q^{\frac{-5}{2}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{-5}{2} - (\frac{-1}{3}) }= q^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ q^{13} }}\\=\frac{1}{|q^{2}|.\sqrt[6]{ q }}=\frac{1}{|q^{2}|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{3}|}\\---------------\)
6. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{-4}{3}}}\\= y^{ \frac{2}{3} - (\frac{-4}{3}) }= y^{2}\\\\---------------\)
7. \(\dfrac{q^{\frac{1}{5}}}{q^{\frac{4}{5}}}\\= q^{ \frac{1}{5} - \frac{4}{5} }= q^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ q^{3} }}=\frac{1}{\sqrt[5]{ q^{3} }}. \color{purple}{\frac{\sqrt[5]{ q^{2} }}{\sqrt[5]{ q^{2} }}} \\=\frac{\sqrt[5]{ q^{2} }}{q}\\---------------\)
8. \(\dfrac{x^{1}}{x^{\frac{-5}{6}}}\\= x^{ 1 - (\frac{-5}{6}) }= x^{\frac{11}{6}}\\=\sqrt[6]{ x^{11} }=|x|.\sqrt[6]{ x^{5} }\\---------------\)
9. \(\dfrac{y^{-1}}{y^{\frac{4}{3}}}\\= y^{ -1 - \frac{4}{3} }= y^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ y^{7} }}\\=\frac{1}{y^{2}.\sqrt[3]{ y }}=\frac{1}{y^{2}.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{3}}\\---------------\)
10. \(\dfrac{x^{\frac{-2}{5}}}{x^{\frac{-3}{2}}}\\= x^{ \frac{-2}{5} - (\frac{-3}{2}) }= x^{\frac{11}{10}}\\=\sqrt[10]{ x^{11} }=|x|.\sqrt[10]{ x }\\---------------\)
11. \(\dfrac{q^{\frac{5}{3}}}{q^{1}}\\= q^{ \frac{5}{3} - 1 }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
12. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{-5}{3}}}\\= q^{ \frac{-1}{3} - (\frac{-5}{3}) }= q^{\frac{4}{3}}\\=\sqrt[3]{ q^{4} }=q.\sqrt[3]{ q }\\---------------\)