Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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