Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-1}{4}}}{a^{\frac{4}{3}}}\\= a^{ \frac{-1}{4} - \frac{4}{3} }= a^{\frac{-19}{12}}\\=\frac{1}{\sqrt[12]{ a^{19} }}\\=\frac{1}{|a|.\sqrt[12]{ a^{7} }}=\frac{1}{|a|.\sqrt[12]{ a^{7} }} \color{purple}{\frac{\sqrt[12]{ a^{5} }}{\sqrt[12]{ a^{5} }}} \\=\frac{\sqrt[12]{ a^{5} }}{|a^{2}|}\\---------------\)
2. \(\dfrac{q^{\frac{1}{5}}}{q^{\frac{2}{5}}}\\= q^{ \frac{1}{5} - \frac{2}{5} }= q^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ q }}=\frac{1}{\sqrt[5]{ q }}. \color{purple}{\frac{\sqrt[5]{ q^{4} }}{\sqrt[5]{ q^{4} }}} \\=\frac{\sqrt[5]{ q^{4} }}{q}\\---------------\)
3. \(\dfrac{y^{\frac{3}{5}}}{y^{-1}}\\= y^{ \frac{3}{5} - (-1) }= y^{\frac{8}{5}}\\=\sqrt[5]{ y^{8} }=y.\sqrt[5]{ y^{3} }\\---------------\)
4. \(\dfrac{a^{\frac{5}{6}}}{a^{\frac{1}{5}}}\\= a^{ \frac{5}{6} - \frac{1}{5} }= a^{\frac{19}{30}}\\=\sqrt[30]{ a^{19} }\\---------------\)
5. \(\dfrac{y^{1}}{y^{\frac{5}{4}}}\\= y^{ 1 - \frac{5}{4} }= y^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ y }}=\frac{1}{\sqrt[4]{ y }}. \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y|}\\---------------\)
6. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{1}{3}}}\\= a^{ \frac{-1}{3} - \frac{1}{3} }= a^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ a^{2} }}=\frac{1}{\sqrt[3]{ a^{2} }}. \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a}\\---------------\)
7. \(\dfrac{y^{\frac{-2}{3}}}{y^{1}}\\= y^{ \frac{-2}{3} - 1 }= y^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ y^{5} }}\\=\frac{1}{y.\sqrt[3]{ y^{2} }}=\frac{1}{y.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{2}}\\---------------\)
8. \(\dfrac{x^{\frac{-5}{2}}}{x^{-2}}\\= x^{ \frac{-5}{2} - (-2) }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
9. \(\dfrac{a^{1}}{a^{\frac{3}{5}}}\\= a^{ 1 - \frac{3}{5} }= a^{\frac{2}{5}}\\=\sqrt[5]{ a^{2} }\\---------------\)
10. \(\dfrac{a^{\frac{5}{2}}}{a^{\frac{5}{3}}}\\= a^{ \frac{5}{2} - \frac{5}{3} }= a^{\frac{5}{6}}\\=\sqrt[6]{ a^{5} }\\---------------\)
11. \(\dfrac{a^{\frac{3}{2}}}{a^{\frac{4}{5}}}\\= a^{ \frac{3}{2} - \frac{4}{5} }= a^{\frac{7}{10}}\\=\sqrt[10]{ a^{7} }\\---------------\)
12. \(\dfrac{q^{\frac{3}{5}}}{q^{\frac{4}{3}}}\\= q^{ \frac{3}{5} - \frac{4}{3} }= q^{\frac{-11}{15}}\\=\frac{1}{\sqrt[15]{ q^{11} }}=\frac{1}{\sqrt[15]{ q^{11} }}. \color{purple}{\frac{\sqrt[15]{ q^{4} }}{\sqrt[15]{ q^{4} }}} \\=\frac{\sqrt[15]{ q^{4} }}{q}\\---------------\)