Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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