Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{5}{3}}}{q^{\frac{1}{4}}}\\= q^{ \frac{5}{3} - \frac{1}{4} }= q^{\frac{17}{12}}\\=\sqrt[12]{ q^{17} }=|q|.\sqrt[12]{ q^{5} }\\---------------\)
2. \(\dfrac{x^{\frac{1}{3}}}{x^{\frac{-1}{5}}}\\= x^{ \frac{1}{3} - (\frac{-1}{5}) }= x^{\frac{8}{15}}\\=\sqrt[15]{ x^{8} }\\---------------\)
3. \(\dfrac{q^{\frac{-5}{2}}}{q^{\frac{2}{3}}}\\= q^{ \frac{-5}{2} - \frac{2}{3} }= q^{\frac{-19}{6}}\\=\frac{1}{\sqrt[6]{ q^{19} }}\\=\frac{1}{|q^{3}|.\sqrt[6]{ q }}=\frac{1}{|q^{3}|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{4}|}\\---------------\)
4. \(\dfrac{x^{\frac{-3}{5}}}{x^{\frac{-4}{5}}}\\= x^{ \frac{-3}{5} - (\frac{-4}{5}) }= x^{\frac{1}{5}}\\=\sqrt[5]{ x }\\---------------\)
5. \(\dfrac{x^{-2}}{x^{\frac{1}{3}}}\\= x^{ -2 - \frac{1}{3} }= x^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ x^{7} }}\\=\frac{1}{x^{2}.\sqrt[3]{ x }}=\frac{1}{x^{2}.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{3}}\\---------------\)
6. \(\dfrac{x^{\frac{5}{3}}}{x^{\frac{5}{4}}}\\= x^{ \frac{5}{3} - \frac{5}{4} }= x^{\frac{5}{12}}\\=\sqrt[12]{ x^{5} }\\---------------\)
7. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{-2}{3} - (\frac{-2}{3}) }= y^{0}\\=1\\---------------\)
8. \(\dfrac{q^{\frac{-3}{2}}}{q^{\frac{-3}{5}}}\\= q^{ \frac{-3}{2} - (\frac{-3}{5}) }= q^{\frac{-9}{10}}\\=\frac{1}{\sqrt[10]{ q^{9} }}=\frac{1}{\sqrt[10]{ q^{9} }}. \color{purple}{\frac{\sqrt[10]{ q }}{\sqrt[10]{ q }}} \\=\frac{\sqrt[10]{ q }}{|q|}\\---------------\)
9. \(\dfrac{a^{\frac{-5}{6}}}{a^{\frac{-5}{2}}}\\= a^{ \frac{-5}{6} - (\frac{-5}{2}) }= a^{\frac{5}{3}}\\=\sqrt[3]{ a^{5} }=a.\sqrt[3]{ a^{2} }\\---------------\)
10. \(\dfrac{x^{\frac{2}{5}}}{x^{-1}}\\= x^{ \frac{2}{5} - (-1) }= x^{\frac{7}{5}}\\=\sqrt[5]{ x^{7} }=x.\sqrt[5]{ x^{2} }\\---------------\)
11. \(\dfrac{a^{\frac{1}{5}}}{a^{1}}\\= a^{ \frac{1}{5} - 1 }= a^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ a^{4} }}=\frac{1}{\sqrt[5]{ a^{4} }}. \color{purple}{\frac{\sqrt[5]{ a }}{\sqrt[5]{ a }}} \\=\frac{\sqrt[5]{ a }}{a}\\---------------\)
12. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{5}{6}}}\\= a^{ \frac{-1}{2} - \frac{5}{6} }= a^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ a^{4} }}\\=\frac{1}{a.\sqrt[3]{ a }}=\frac{1}{a.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{2}}\\---------------\)