Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{1}{6}}}{a^{\frac{-3}{5}}}\\= a^{ \frac{1}{6} - (\frac{-3}{5}) }= a^{\frac{23}{30}}\\=\sqrt[30]{ a^{23} }\\---------------\)
2. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{-3}{5}}}\\= q^{ \frac{2}{3} - (\frac{-3}{5}) }= q^{\frac{19}{15}}\\=\sqrt[15]{ q^{19} }=q.\sqrt[15]{ q^{4} }\\---------------\)
3. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{-3}{5}}}\\= y^{ \frac{-1}{2} - (\frac{-3}{5}) }= y^{\frac{1}{10}}\\=\sqrt[10]{ y }\\---------------\)
4. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{4}{5}}}\\= y^{ \frac{-2}{3} - \frac{4}{5} }= y^{\frac{-22}{15}}\\=\frac{1}{\sqrt[15]{ y^{22} }}\\=\frac{1}{y.\sqrt[15]{ y^{7} }}=\frac{1}{y.\sqrt[15]{ y^{7} }} \color{purple}{\frac{\sqrt[15]{ y^{8} }}{\sqrt[15]{ y^{8} }}} \\=\frac{\sqrt[15]{ y^{8} }}{y^{2}}\\---------------\)
5. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{-5}{2}}}\\= a^{ \frac{1}{3} - (\frac{-5}{2}) }= a^{\frac{17}{6}}\\=\sqrt[6]{ a^{17} }=|a^{2}|.\sqrt[6]{ a^{5} }\\---------------\)
6. \(\dfrac{q^{\frac{-4}{5}}}{q^{\frac{-5}{2}}}\\= q^{ \frac{-4}{5} - (\frac{-5}{2}) }= q^{\frac{17}{10}}\\=\sqrt[10]{ q^{17} }=|q|.\sqrt[10]{ q^{7} }\\---------------\)
7. \(\dfrac{y^{\frac{-4}{5}}}{y^{\frac{1}{3}}}\\= y^{ \frac{-4}{5} - \frac{1}{3} }= y^{\frac{-17}{15}}\\=\frac{1}{\sqrt[15]{ y^{17} }}\\=\frac{1}{y.\sqrt[15]{ y^{2} }}=\frac{1}{y.\sqrt[15]{ y^{2} }} \color{purple}{\frac{\sqrt[15]{ y^{13} }}{\sqrt[15]{ y^{13} }}} \\=\frac{\sqrt[15]{ y^{13} }}{y^{2}}\\---------------\)
8. \(\dfrac{x^{\frac{1}{6}}}{x^{\frac{1}{5}}}\\= x^{ \frac{1}{6} - \frac{1}{5} }= x^{\frac{-1}{30}}\\=\frac{1}{\sqrt[30]{ x }}=\frac{1}{\sqrt[30]{ x }}. \color{purple}{\frac{\sqrt[30]{ x^{29} }}{\sqrt[30]{ x^{29} }}} \\=\frac{\sqrt[30]{ x^{29} }}{|x|}\\---------------\)
9. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{5}{6}}}\\= q^{ \frac{-1}{2} - \frac{5}{6} }= q^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ q^{4} }}\\=\frac{1}{q.\sqrt[3]{ q }}=\frac{1}{q.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{2}}\\---------------\)
10. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{-1}{2} - (\frac{-1}{3}) }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)
11. \(\dfrac{q^{\frac{1}{4}}}{q^{-1}}\\= q^{ \frac{1}{4} - (-1) }= q^{\frac{5}{4}}\\=\sqrt[4]{ q^{5} }=|q|.\sqrt[4]{ q }\\---------------\)
12. \(\dfrac{y^{\frac{1}{6}}}{y^{\frac{5}{4}}}\\= y^{ \frac{1}{6} - \frac{5}{4} }= y^{\frac{-13}{12}}\\=\frac{1}{\sqrt[12]{ y^{13} }}\\=\frac{1}{|y|.\sqrt[12]{ y }}=\frac{1}{|y|.\sqrt[12]{ y }} \color{purple}{\frac{\sqrt[12]{ y^{11} }}{\sqrt[12]{ y^{11} }}} \\=\frac{\sqrt[12]{ y^{11} }}{|y^{2}|}\\---------------\)