Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-1}{5}}}{x^{\frac{-2}{3}}}\\= x^{ \frac{-1}{5} - (\frac{-2}{3}) }= x^{\frac{7}{15}}\\=\sqrt[15]{ x^{7} }\\---------------\)
2. \(\dfrac{a^{\frac{-1}{4}}}{a^{\frac{2}{3}}}\\= a^{ \frac{-1}{4} - \frac{2}{3} }= a^{\frac{-11}{12}}\\=\frac{1}{\sqrt[12]{ a^{11} }}=\frac{1}{\sqrt[12]{ a^{11} }}. \color{purple}{\frac{\sqrt[12]{ a }}{\sqrt[12]{ a }}} \\=\frac{\sqrt[12]{ a }}{|a|}\\---------------\)
3. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{1}{2}}}\\= q^{ \frac{-2}{3} - \frac{1}{2} }= q^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ q^{7} }}\\=\frac{1}{|q|.\sqrt[6]{ q }}=\frac{1}{|q|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{2}|}\\---------------\)
4. \(\dfrac{a^{\frac{-3}{4}}}{a^{\frac{-5}{6}}}\\= a^{ \frac{-3}{4} - (\frac{-5}{6}) }= a^{\frac{1}{12}}\\=\sqrt[12]{ a }\\---------------\)
5. \(\dfrac{a^{\frac{3}{4}}}{a^{\frac{1}{3}}}\\= a^{ \frac{3}{4} - \frac{1}{3} }= a^{\frac{5}{12}}\\=\sqrt[12]{ a^{5} }\\---------------\)
6. \(\dfrac{a^{\frac{2}{5}}}{a^{\frac{2}{3}}}\\= a^{ \frac{2}{5} - \frac{2}{3} }= a^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ a^{4} }}=\frac{1}{\sqrt[15]{ a^{4} }}. \color{purple}{\frac{\sqrt[15]{ a^{11} }}{\sqrt[15]{ a^{11} }}} \\=\frac{\sqrt[15]{ a^{11} }}{a}\\---------------\)
7. \(\dfrac{x^{1}}{x^{-2}}\\= x^{ 1 - (-2) }= x^{3}\\\\---------------\)
8. \(\dfrac{y^{\frac{5}{4}}}{y^{1}}\\= y^{ \frac{5}{4} - 1 }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)
9. \(\dfrac{q^{-2}}{q^{\frac{-3}{2}}}\\= q^{ -2 - (\frac{-3}{2}) }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
10. \(\dfrac{y^{\frac{-1}{2}}}{y^{1}}\\= y^{ \frac{-1}{2} - 1 }= y^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ y^{3} } }\\=\frac{1}{|y|. \sqrt{ y } }=\frac{1}{|y|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{2}|}\\---------------\)
11. \(\dfrac{y^{\frac{4}{5}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{4}{5} - (\frac{-2}{3}) }= y^{\frac{22}{15}}\\=\sqrt[15]{ y^{22} }=y.\sqrt[15]{ y^{7} }\\---------------\)
12. \(\dfrac{a^{\frac{-3}{5}}}{a^{-1}}\\= a^{ \frac{-3}{5} - (-1) }= a^{\frac{2}{5}}\\=\sqrt[5]{ a^{2} }\\---------------\)