Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-5}{3}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{-5}{3} - (\frac{-1}{2}) }= q^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ q^{7} }}\\=\frac{1}{|q|.\sqrt[6]{ q }}=\frac{1}{|q|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{2}|}\\---------------\)
2. \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{5}{3}}}\\= x^{ \frac{-2}{3} - \frac{5}{3} }= x^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ x^{7} }}\\=\frac{1}{x^{2}.\sqrt[3]{ x }}=\frac{1}{x^{2}.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{3}}\\---------------\)
3. \(\dfrac{a^{-2}}{a^{\frac{1}{6}}}\\= a^{ -2 - \frac{1}{6} }= a^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ a^{13} }}\\=\frac{1}{|a^{2}|.\sqrt[6]{ a }}=\frac{1}{|a^{2}|.\sqrt[6]{ a }} \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a^{3}|}\\---------------\)
4. \(\dfrac{q^{\frac{4}{5}}}{q^{\frac{3}{2}}}\\= q^{ \frac{4}{5} - \frac{3}{2} }= q^{\frac{-7}{10}}\\=\frac{1}{\sqrt[10]{ q^{7} }}=\frac{1}{\sqrt[10]{ q^{7} }}. \color{purple}{\frac{\sqrt[10]{ q^{3} }}{\sqrt[10]{ q^{3} }}} \\=\frac{\sqrt[10]{ q^{3} }}{|q|}\\---------------\)
5. \(\dfrac{q^{\frac{5}{6}}}{q^{-1}}\\= q^{ \frac{5}{6} - (-1) }= q^{\frac{11}{6}}\\=\sqrt[6]{ q^{11} }=|q|.\sqrt[6]{ q^{5} }\\---------------\)
6. \(\dfrac{x^{1}}{x^{\frac{-4}{3}}}\\= x^{ 1 - (\frac{-4}{3}) }= x^{\frac{7}{3}}\\=\sqrt[3]{ x^{7} }=x^{2}.\sqrt[3]{ x }\\---------------\)
7. \(\dfrac{y^{\frac{1}{2}}}{y^{1}}\\= y^{ \frac{1}{2} - 1 }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
8. \(\dfrac{a^{\frac{3}{2}}}{a^{\frac{1}{3}}}\\= a^{ \frac{3}{2} - \frac{1}{3} }= a^{\frac{7}{6}}\\=\sqrt[6]{ a^{7} }=|a|.\sqrt[6]{ a }\\---------------\)
9. \(\dfrac{x^{\frac{-5}{4}}}{x^{\frac{1}{5}}}\\= x^{ \frac{-5}{4} - \frac{1}{5} }= x^{\frac{-29}{20}}\\=\frac{1}{\sqrt[20]{ x^{29} }}\\=\frac{1}{|x|.\sqrt[20]{ x^{9} }}=\frac{1}{|x|.\sqrt[20]{ x^{9} }} \color{purple}{\frac{\sqrt[20]{ x^{11} }}{\sqrt[20]{ x^{11} }}} \\=\frac{\sqrt[20]{ x^{11} }}{|x^{2}|}\\---------------\)
10. \(\dfrac{y^{\frac{-4}{5}}}{y^{1}}\\= y^{ \frac{-4}{5} - 1 }= y^{\frac{-9}{5}}\\=\frac{1}{\sqrt[5]{ y^{9} }}\\=\frac{1}{y.\sqrt[5]{ y^{4} }}=\frac{1}{y.\sqrt[5]{ y^{4} }} \color{purple}{\frac{\sqrt[5]{ y }}{\sqrt[5]{ y }}} \\=\frac{\sqrt[5]{ y }}{y^{2}}\\---------------\)
11. \(\dfrac{a^{-2}}{a^{\frac{3}{5}}}\\= a^{ -2 - \frac{3}{5} }= a^{\frac{-13}{5}}\\=\frac{1}{\sqrt[5]{ a^{13} }}\\=\frac{1}{a^{2}.\sqrt[5]{ a^{3} }}=\frac{1}{a^{2}.\sqrt[5]{ a^{3} }} \color{purple}{\frac{\sqrt[5]{ a^{2} }}{\sqrt[5]{ a^{2} }}} \\=\frac{\sqrt[5]{ a^{2} }}{a^{3}}\\---------------\)
12. \(\dfrac{x^{\frac{1}{5}}}{x^{\frac{-1}{5}}}\\= x^{ \frac{1}{5} - (\frac{-1}{5}) }= x^{\frac{2}{5}}\\=\sqrt[5]{ x^{2} }\\---------------\)