Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-1}{5}}}{q^{\frac{-5}{2}}}\\= q^{ \frac{-1}{5} - (\frac{-5}{2}) }= q^{\frac{23}{10}}\\=\sqrt[10]{ q^{23} }=|q^{2}|.\sqrt[10]{ q^{3} }\\---------------\)
2. \(\dfrac{a^{\frac{1}{4}}}{a^{\frac{2}{5}}}\\= a^{ \frac{1}{4} - \frac{2}{5} }= a^{\frac{-3}{20}}\\=\frac{1}{\sqrt[20]{ a^{3} }}=\frac{1}{\sqrt[20]{ a^{3} }}. \color{purple}{\frac{\sqrt[20]{ a^{17} }}{\sqrt[20]{ a^{17} }}} \\=\frac{\sqrt[20]{ a^{17} }}{|a|}\\---------------\)
3. \(\dfrac{a^{-1}}{a^{\frac{1}{4}}}\\= a^{ -1 - \frac{1}{4} }= a^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ a^{5} }}\\=\frac{1}{|a|.\sqrt[4]{ a }}=\frac{1}{|a|.\sqrt[4]{ a }} \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a^{2}|}\\---------------\)
4. \(\dfrac{y^{\frac{4}{5}}}{y^{\frac{1}{3}}}\\= y^{ \frac{4}{5} - \frac{1}{3} }= y^{\frac{7}{15}}\\=\sqrt[15]{ y^{7} }\\---------------\)
5. \(\dfrac{y^{-1}}{y^{\frac{-2}{3}}}\\= y^{ -1 - (\frac{-2}{3}) }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
6. \(\dfrac{y^{\frac{1}{4}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{1}{4} - (\frac{-1}{2}) }= y^{\frac{3}{4}}\\=\sqrt[4]{ y^{3} }\\---------------\)
7. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{-5}{6}}}\\= a^{ \frac{1}{3} - (\frac{-5}{6}) }= a^{\frac{7}{6}}\\=\sqrt[6]{ a^{7} }=|a|.\sqrt[6]{ a }\\---------------\)
8. \(\dfrac{a^{\frac{-5}{2}}}{a^{\frac{5}{6}}}\\= a^{ \frac{-5}{2} - \frac{5}{6} }= a^{\frac{-10}{3}}\\=\frac{1}{\sqrt[3]{ a^{10} }}\\=\frac{1}{a^{3}.\sqrt[3]{ a }}=\frac{1}{a^{3}.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{4}}\\---------------\)
9. \(\dfrac{q^{\frac{3}{5}}}{q^{-1}}\\= q^{ \frac{3}{5} - (-1) }= q^{\frac{8}{5}}\\=\sqrt[5]{ q^{8} }=q.\sqrt[5]{ q^{3} }\\---------------\)
10. \(\dfrac{q^{-2}}{q^{\frac{-3}{2}}}\\= q^{ -2 - (\frac{-3}{2}) }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
11. \(\dfrac{q^{\frac{1}{5}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{1}{5} - (\frac{-1}{2}) }= q^{\frac{7}{10}}\\=\sqrt[10]{ q^{7} }\\---------------\)
12. \(\dfrac{x^{\frac{-1}{4}}}{x^{\frac{-1}{6}}}\\= x^{ \frac{-1}{4} - (\frac{-1}{6}) }= x^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ x }}=\frac{1}{\sqrt[12]{ x }}. \color{purple}{\frac{\sqrt[12]{ x^{11} }}{\sqrt[12]{ x^{11} }}} \\=\frac{\sqrt[12]{ x^{11} }}{|x|}\\---------------\)