Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{-3}{2}}}\\= y^{ \frac{-1}{2} - (\frac{-3}{2}) }= y^{1}\\\\---------------\)
2. \(\dfrac{q^{\frac{-4}{5}}}{q^{\frac{1}{2}}}\\= q^{ \frac{-4}{5} - \frac{1}{2} }= q^{\frac{-13}{10}}\\=\frac{1}{\sqrt[10]{ q^{13} }}\\=\frac{1}{|q|.\sqrt[10]{ q^{3} }}=\frac{1}{|q|.\sqrt[10]{ q^{3} }} \color{purple}{\frac{\sqrt[10]{ q^{7} }}{\sqrt[10]{ q^{7} }}} \\=\frac{\sqrt[10]{ q^{7} }}{|q^{2}|}\\---------------\)
3. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{2}{3} - (\frac{-1}{2}) }= q^{\frac{7}{6}}\\=\sqrt[6]{ q^{7} }=|q|.\sqrt[6]{ q }\\---------------\)
4. \(\dfrac{q^{\frac{-3}{2}}}{q^{\frac{3}{2}}}\\= q^{ \frac{-3}{2} - \frac{3}{2} }= q^{-3}\\=\frac{1}{q^{3}}\\---------------\)
5. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{3}{5}}}\\= a^{ \frac{-1}{2} - \frac{3}{5} }= a^{\frac{-11}{10}}\\=\frac{1}{\sqrt[10]{ a^{11} }}\\=\frac{1}{|a|.\sqrt[10]{ a }}=\frac{1}{|a|.\sqrt[10]{ a }} \color{purple}{\frac{\sqrt[10]{ a^{9} }}{\sqrt[10]{ a^{9} }}} \\=\frac{\sqrt[10]{ a^{9} }}{|a^{2}|}\\---------------\)
6. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{2}{5}}}\\= q^{ \frac{-2}{3} - \frac{2}{5} }= q^{\frac{-16}{15}}\\=\frac{1}{\sqrt[15]{ q^{16} }}\\=\frac{1}{q.\sqrt[15]{ q }}=\frac{1}{q.\sqrt[15]{ q }} \color{purple}{\frac{\sqrt[15]{ q^{14} }}{\sqrt[15]{ q^{14} }}} \\=\frac{\sqrt[15]{ q^{14} }}{q^{2}}\\---------------\)
7. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{4}{5}}}\\= q^{ \frac{1}{2} - \frac{4}{5} }= q^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ q^{3} }}=\frac{1}{\sqrt[10]{ q^{3} }}. \color{purple}{\frac{\sqrt[10]{ q^{7} }}{\sqrt[10]{ q^{7} }}} \\=\frac{\sqrt[10]{ q^{7} }}{|q|}\\---------------\)
8. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{4}{3}}}\\= y^{ \frac{-1}{3} - \frac{4}{3} }= y^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ y^{5} }}\\=\frac{1}{y.\sqrt[3]{ y^{2} }}=\frac{1}{y.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{2}}\\---------------\)
9. \(\dfrac{x^{1}}{x^{\frac{-2}{3}}}\\= x^{ 1 - (\frac{-2}{3}) }= x^{\frac{5}{3}}\\=\sqrt[3]{ x^{5} }=x.\sqrt[3]{ x^{2} }\\---------------\)
10. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{-1}{6}}}\\= x^{ \frac{-1}{3} - (\frac{-1}{6}) }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
11. \(\dfrac{y^{2}}{y^{\frac{-3}{2}}}\\= y^{ 2 - (\frac{-3}{2}) }= y^{\frac{7}{2}}\\= \sqrt{ y^{7} } =|y^{3}|. \sqrt{ y } \\---------------\)
12. \(\dfrac{y^{\frac{-5}{3}}}{y^{\frac{2}{3}}}\\= y^{ \frac{-5}{3} - \frac{2}{3} }= y^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ y^{7} }}\\=\frac{1}{y^{2}.\sqrt[3]{ y }}=\frac{1}{y^{2}.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{3}}\\---------------\)