Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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