Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{5}{4}}}\\= q^{ \frac{-1}{2} - \frac{5}{4} }= q^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ q^{7} }}\\=\frac{1}{|q|.\sqrt[4]{ q^{3} }}=\frac{1}{|q|.\sqrt[4]{ q^{3} }} \color{purple}{\frac{\sqrt[4]{ q }}{\sqrt[4]{ q }}} \\=\frac{\sqrt[4]{ q }}{|q^{2}|}\\---------------\)
2. \(\dfrac{x^{\frac{-4}{3}}}{x^{-2}}\\= x^{ \frac{-4}{3} - (-2) }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
3. \(\dfrac{x^{\frac{-5}{6}}}{x^{\frac{5}{6}}}\\= x^{ \frac{-5}{6} - \frac{5}{6} }= x^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ x^{5} }}\\=\frac{1}{x.\sqrt[3]{ x^{2} }}=\frac{1}{x.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{2}}\\---------------\)
4. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{-2}{3} - (\frac{-1}{3}) }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
5. \(\dfrac{a^{\frac{4}{5}}}{a^{-1}}\\= a^{ \frac{4}{5} - (-1) }= a^{\frac{9}{5}}\\=\sqrt[5]{ a^{9} }=a.\sqrt[5]{ a^{4} }\\---------------\)
6. \(\dfrac{y^{\frac{-4}{3}}}{y^{\frac{3}{2}}}\\= y^{ \frac{-4}{3} - \frac{3}{2} }= y^{\frac{-17}{6}}\\=\frac{1}{\sqrt[6]{ y^{17} }}\\=\frac{1}{|y^{2}|.\sqrt[6]{ y^{5} }}=\frac{1}{|y^{2}|.\sqrt[6]{ y^{5} }} \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y^{3}|}\\---------------\)
7. \(\dfrac{a^{\frac{-5}{4}}}{a^{\frac{2}{5}}}\\= a^{ \frac{-5}{4} - \frac{2}{5} }= a^{\frac{-33}{20}}\\=\frac{1}{\sqrt[20]{ a^{33} }}\\=\frac{1}{|a|.\sqrt[20]{ a^{13} }}=\frac{1}{|a|.\sqrt[20]{ a^{13} }} \color{purple}{\frac{\sqrt[20]{ a^{7} }}{\sqrt[20]{ a^{7} }}} \\=\frac{\sqrt[20]{ a^{7} }}{|a^{2}|}\\---------------\)
8. \(\dfrac{x^{\frac{-1}{5}}}{x^{\frac{1}{6}}}\\= x^{ \frac{-1}{5} - \frac{1}{6} }= x^{\frac{-11}{30}}\\=\frac{1}{\sqrt[30]{ x^{11} }}=\frac{1}{\sqrt[30]{ x^{11} }}. \color{purple}{\frac{\sqrt[30]{ x^{19} }}{\sqrt[30]{ x^{19} }}} \\=\frac{\sqrt[30]{ x^{19} }}{|x|}\\---------------\)
9. \(\dfrac{x^{1}}{x^{\frac{-1}{3}}}\\= x^{ 1 - (\frac{-1}{3}) }= x^{\frac{4}{3}}\\=\sqrt[3]{ x^{4} }=x.\sqrt[3]{ x }\\---------------\)
10. \(\dfrac{x^{-1}}{x^{\frac{1}{2}}}\\= x^{ -1 - \frac{1}{2} }= x^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ x^{3} } }\\=\frac{1}{|x|. \sqrt{ x } }=\frac{1}{|x|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{2}|}\\---------------\)
11. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{-1}{5}}}\\= x^{ \frac{-1}{3} - (\frac{-1}{5}) }= x^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ x^{2} }}=\frac{1}{\sqrt[15]{ x^{2} }}. \color{purple}{\frac{\sqrt[15]{ x^{13} }}{\sqrt[15]{ x^{13} }}} \\=\frac{\sqrt[15]{ x^{13} }}{x}\\---------------\)
12. \(\dfrac{a^{1}}{a^{\frac{-5}{4}}}\\= a^{ 1 - (\frac{-5}{4}) }= a^{\frac{9}{4}}\\=\sqrt[4]{ a^{9} }=|a^{2}|.\sqrt[4]{ a }\\---------------\)