Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{-2}{5}}}\\= q^{ \frac{-1}{2} - (\frac{-2}{5}) }= q^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ q }}=\frac{1}{\sqrt[10]{ q }}. \color{purple}{\frac{\sqrt[10]{ q^{9} }}{\sqrt[10]{ q^{9} }}} \\=\frac{\sqrt[10]{ q^{9} }}{|q|}\\---------------\)
2. \(\dfrac{q^{\frac{-3}{2}}}{q^{\frac{3}{5}}}\\= q^{ \frac{-3}{2} - \frac{3}{5} }= q^{\frac{-21}{10}}\\=\frac{1}{\sqrt[10]{ q^{21} }}\\=\frac{1}{|q^{2}|.\sqrt[10]{ q }}=\frac{1}{|q^{2}|.\sqrt[10]{ q }} \color{purple}{\frac{\sqrt[10]{ q^{9} }}{\sqrt[10]{ q^{9} }}} \\=\frac{\sqrt[10]{ q^{9} }}{|q^{3}|}\\---------------\)
3. \(\dfrac{a^{\frac{5}{3}}}{a^{\frac{-5}{4}}}\\= a^{ \frac{5}{3} - (\frac{-5}{4}) }= a^{\frac{35}{12}}\\=\sqrt[12]{ a^{35} }=|a^{2}|.\sqrt[12]{ a^{11} }\\---------------\)
4. \(\dfrac{x^{\frac{1}{4}}}{x^{\frac{2}{3}}}\\= x^{ \frac{1}{4} - \frac{2}{3} }= x^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ x^{5} }}=\frac{1}{\sqrt[12]{ x^{5} }}. \color{purple}{\frac{\sqrt[12]{ x^{7} }}{\sqrt[12]{ x^{7} }}} \\=\frac{\sqrt[12]{ x^{7} }}{|x|}\\---------------\)
5. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{5}{3}}}\\= q^{ \frac{1}{2} - \frac{5}{3} }= q^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ q^{7} }}\\=\frac{1}{|q|.\sqrt[6]{ q }}=\frac{1}{|q|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{2}|}\\---------------\)
6. \(\dfrac{y^{\frac{-4}{5}}}{y^{\frac{-1}{4}}}\\= y^{ \frac{-4}{5} - (\frac{-1}{4}) }= y^{\frac{-11}{20}}\\=\frac{1}{\sqrt[20]{ y^{11} }}=\frac{1}{\sqrt[20]{ y^{11} }}. \color{purple}{\frac{\sqrt[20]{ y^{9} }}{\sqrt[20]{ y^{9} }}} \\=\frac{\sqrt[20]{ y^{9} }}{|y|}\\---------------\)
7. \(\dfrac{q^{\frac{-5}{3}}}{q^{\frac{3}{2}}}\\= q^{ \frac{-5}{3} - \frac{3}{2} }= q^{\frac{-19}{6}}\\=\frac{1}{\sqrt[6]{ q^{19} }}\\=\frac{1}{|q^{3}|.\sqrt[6]{ q }}=\frac{1}{|q^{3}|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{4}|}\\---------------\)
8. \(\dfrac{q^{\frac{-4}{5}}}{q^{\frac{2}{3}}}\\= q^{ \frac{-4}{5} - \frac{2}{3} }= q^{\frac{-22}{15}}\\=\frac{1}{\sqrt[15]{ q^{22} }}\\=\frac{1}{q.\sqrt[15]{ q^{7} }}=\frac{1}{q.\sqrt[15]{ q^{7} }} \color{purple}{\frac{\sqrt[15]{ q^{8} }}{\sqrt[15]{ q^{8} }}} \\=\frac{\sqrt[15]{ q^{8} }}{q^{2}}\\---------------\)
9. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{-1}{3} - (\frac{-1}{3}) }= y^{0}\\=1\\---------------\)
10. \(\dfrac{x^{\frac{-5}{6}}}{x^{-1}}\\= x^{ \frac{-5}{6} - (-1) }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
11. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{-3}{2}}}\\= y^{ \frac{-1}{2} - (\frac{-3}{2}) }= y^{1}\\\\---------------\)
12. \(\dfrac{y^{-2}}{y^{2}}\\= y^{ -2 - 2 }= y^{-4}\\=\frac{1}{y^{4}}\\---------------\)