Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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