Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-4}{5}}}{y^{\frac{1}{3}}}\\= y^{ \frac{-4}{5} - \frac{1}{3} }= y^{\frac{-17}{15}}\\=\frac{1}{\sqrt[15]{ y^{17} }}\\=\frac{1}{y.\sqrt[15]{ y^{2} }}=\frac{1}{y.\sqrt[15]{ y^{2} }} \color{purple}{\frac{\sqrt[15]{ y^{13} }}{\sqrt[15]{ y^{13} }}} \\=\frac{\sqrt[15]{ y^{13} }}{y^{2}}\\---------------\)
2. \(\dfrac{q^{\frac{-5}{4}}}{q^{\frac{-1}{4}}}\\= q^{ \frac{-5}{4} - (\frac{-1}{4}) }= q^{-1}\\=\frac{1}{q}\\---------------\)
3. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{-2}{3} - (\frac{-1}{2}) }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)
4. \(\dfrac{x^{\frac{-4}{5}}}{x^{-2}}\\= x^{ \frac{-4}{5} - (-2) }= x^{\frac{6}{5}}\\=\sqrt[5]{ x^{6} }=x.\sqrt[5]{ x }\\---------------\)
5. \(\dfrac{a^{\frac{3}{5}}}{a^{\frac{2}{3}}}\\= a^{ \frac{3}{5} - \frac{2}{3} }= a^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ a }}=\frac{1}{\sqrt[15]{ a }}. \color{purple}{\frac{\sqrt[15]{ a^{14} }}{\sqrt[15]{ a^{14} }}} \\=\frac{\sqrt[15]{ a^{14} }}{a}\\---------------\)
6. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{-1}{6}}}\\= q^{ \frac{-1}{3} - (\frac{-1}{6}) }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)
7. \(\dfrac{x^{\frac{1}{3}}}{x^{\frac{-3}{5}}}\\= x^{ \frac{1}{3} - (\frac{-3}{5}) }= x^{\frac{14}{15}}\\=\sqrt[15]{ x^{14} }\\---------------\)
8. \(\dfrac{a^{\frac{-5}{3}}}{a^{\frac{1}{3}}}\\= a^{ \frac{-5}{3} - \frac{1}{3} }= a^{-2}\\=\frac{1}{a^{2}}\\---------------\)
9. \(\dfrac{x^{\frac{5}{4}}}{x^{-1}}\\= x^{ \frac{5}{4} - (-1) }= x^{\frac{9}{4}}\\=\sqrt[4]{ x^{9} }=|x^{2}|.\sqrt[4]{ x }\\---------------\)
10. \(\dfrac{y^{\frac{1}{3}}}{y^{\frac{1}{3}}}\\= y^{ \frac{1}{3} - \frac{1}{3} }= y^{0}\\=1\\---------------\)
11. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{5}{3}}}\\= q^{ \frac{-2}{3} - \frac{5}{3} }= q^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ q^{7} }}\\=\frac{1}{q^{2}.\sqrt[3]{ q }}=\frac{1}{q^{2}.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{3}}\\---------------\)
12. \(\dfrac{y^{\frac{1}{5}}}{y^{-1}}\\= y^{ \frac{1}{5} - (-1) }= y^{\frac{6}{5}}\\=\sqrt[5]{ y^{6} }=y.\sqrt[5]{ y }\\---------------\)