Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{-1}}{a^{\frac{-5}{6}}}\\= a^{ -1 - (\frac{-5}{6}) }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
2. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{2}{3}}}\\= q^{ \frac{1}{2} - \frac{2}{3} }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)
3. \(\dfrac{q^{\frac{2}{5}}}{q^{\frac{3}{4}}}\\= q^{ \frac{2}{5} - \frac{3}{4} }= q^{\frac{-7}{20}}\\=\frac{1}{\sqrt[20]{ q^{7} }}=\frac{1}{\sqrt[20]{ q^{7} }}. \color{purple}{\frac{\sqrt[20]{ q^{13} }}{\sqrt[20]{ q^{13} }}} \\=\frac{\sqrt[20]{ q^{13} }}{|q|}\\---------------\)
4. \(\dfrac{y^{\frac{-1}{5}}}{y^{1}}\\= y^{ \frac{-1}{5} - 1 }= y^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ y^{6} }}\\=\frac{1}{y.\sqrt[5]{ y }}=\frac{1}{y.\sqrt[5]{ y }} \color{purple}{\frac{\sqrt[5]{ y^{4} }}{\sqrt[5]{ y^{4} }}} \\=\frac{\sqrt[5]{ y^{4} }}{y^{2}}\\---------------\)
5. \(\dfrac{y^{\frac{-5}{4}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{-5}{4} - (\frac{-1}{2}) }= y^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ y^{3} }}=\frac{1}{\sqrt[4]{ y^{3} }}. \color{purple}{\frac{\sqrt[4]{ y }}{\sqrt[4]{ y }}} \\=\frac{\sqrt[4]{ y }}{|y|}\\---------------\)
6. \(\dfrac{x^{\frac{-2}{5}}}{x^{\frac{-1}{5}}}\\= x^{ \frac{-2}{5} - (\frac{-1}{5}) }= x^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ x }}=\frac{1}{\sqrt[5]{ x }}. \color{purple}{\frac{\sqrt[5]{ x^{4} }}{\sqrt[5]{ x^{4} }}} \\=\frac{\sqrt[5]{ x^{4} }}{x}\\---------------\)
7. \(\dfrac{q^{\frac{4}{5}}}{q^{1}}\\= q^{ \frac{4}{5} - 1 }= q^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ q }}=\frac{1}{\sqrt[5]{ q }}. \color{purple}{\frac{\sqrt[5]{ q^{4} }}{\sqrt[5]{ q^{4} }}} \\=\frac{\sqrt[5]{ q^{4} }}{q}\\---------------\)
8. \(\dfrac{q^{\frac{4}{3}}}{q^{\frac{1}{3}}}\\= q^{ \frac{4}{3} - \frac{1}{3} }= q^{1}\\\\---------------\)
9. \(\dfrac{q^{\frac{-3}{2}}}{q^{\frac{2}{5}}}\\= q^{ \frac{-3}{2} - \frac{2}{5} }= q^{\frac{-19}{10}}\\=\frac{1}{\sqrt[10]{ q^{19} }}\\=\frac{1}{|q|.\sqrt[10]{ q^{9} }}=\frac{1}{|q|.\sqrt[10]{ q^{9} }} \color{purple}{\frac{\sqrt[10]{ q }}{\sqrt[10]{ q }}} \\=\frac{\sqrt[10]{ q }}{|q^{2}|}\\---------------\)
10. \(\dfrac{a^{\frac{-4}{5}}}{a^{\frac{2}{3}}}\\= a^{ \frac{-4}{5} - \frac{2}{3} }= a^{\frac{-22}{15}}\\=\frac{1}{\sqrt[15]{ a^{22} }}\\=\frac{1}{a.\sqrt[15]{ a^{7} }}=\frac{1}{a.\sqrt[15]{ a^{7} }} \color{purple}{\frac{\sqrt[15]{ a^{8} }}{\sqrt[15]{ a^{8} }}} \\=\frac{\sqrt[15]{ a^{8} }}{a^{2}}\\---------------\)
11. \(\dfrac{q^{\frac{-5}{3}}}{q^{\frac{1}{2}}}\\= q^{ \frac{-5}{3} - \frac{1}{2} }= q^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ q^{13} }}\\=\frac{1}{|q^{2}|.\sqrt[6]{ q }}=\frac{1}{|q^{2}|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{3}|}\\---------------\)
12. \(\dfrac{x^{\frac{-3}{2}}}{x^{\frac{4}{3}}}\\= x^{ \frac{-3}{2} - \frac{4}{3} }= x^{\frac{-17}{6}}\\=\frac{1}{\sqrt[6]{ x^{17} }}\\=\frac{1}{|x^{2}|.\sqrt[6]{ x^{5} }}=\frac{1}{|x^{2}|.\sqrt[6]{ x^{5} }} \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x^{3}|}\\---------------\)