Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{4}{3}}}{q^{-1}}\\= q^{ \frac{4}{3} - (-1) }= q^{\frac{7}{3}}\\=\sqrt[3]{ q^{7} }=q^{2}.\sqrt[3]{ q }\\---------------\)
2. \(\dfrac{q^{\frac{3}{2}}}{q^{1}}\\= q^{ \frac{3}{2} - 1 }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
3. \(\dfrac{y^{\frac{3}{4}}}{y^{\frac{4}{5}}}\\= y^{ \frac{3}{4} - \frac{4}{5} }= y^{\frac{-1}{20}}\\=\frac{1}{\sqrt[20]{ y }}=\frac{1}{\sqrt[20]{ y }}. \color{purple}{\frac{\sqrt[20]{ y^{19} }}{\sqrt[20]{ y^{19} }}} \\=\frac{\sqrt[20]{ y^{19} }}{|y|}\\---------------\)
4. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{2}{5}}}\\= q^{ \frac{1}{3} - \frac{2}{5} }= q^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ q }}=\frac{1}{\sqrt[15]{ q }}. \color{purple}{\frac{\sqrt[15]{ q^{14} }}{\sqrt[15]{ q^{14} }}} \\=\frac{\sqrt[15]{ q^{14} }}{q}\\---------------\)
5. \(\dfrac{q^{\frac{-2}{5}}}{q^{\frac{-3}{4}}}\\= q^{ \frac{-2}{5} - (\frac{-3}{4}) }= q^{\frac{7}{20}}\\=\sqrt[20]{ q^{7} }\\---------------\)
6. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{-1}{5}}}\\= y^{ \frac{-1}{2} - (\frac{-1}{5}) }= y^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ y^{3} }}=\frac{1}{\sqrt[10]{ y^{3} }}. \color{purple}{\frac{\sqrt[10]{ y^{7} }}{\sqrt[10]{ y^{7} }}} \\=\frac{\sqrt[10]{ y^{7} }}{|y|}\\---------------\)
7. \(\dfrac{x^{1}}{x^{\frac{2}{3}}}\\= x^{ 1 - \frac{2}{3} }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
8. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{-4}{5}}}\\= q^{ \frac{-1}{2} - (\frac{-4}{5}) }= q^{\frac{3}{10}}\\=\sqrt[10]{ q^{3} }\\---------------\)
9. \(\dfrac{a^{\frac{5}{2}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{5}{2} - (\frac{-1}{2}) }= a^{3}\\\\---------------\)
10. \(\dfrac{y^{\frac{3}{2}}}{y^{-1}}\\= y^{ \frac{3}{2} - (-1) }= y^{\frac{5}{2}}\\= \sqrt{ y^{5} } =|y^{2}|. \sqrt{ y } \\---------------\)
11. \(\dfrac{y^{\frac{1}{4}}}{y^{\frac{3}{2}}}\\= y^{ \frac{1}{4} - \frac{3}{2} }= y^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ y^{5} }}\\=\frac{1}{|y|.\sqrt[4]{ y }}=\frac{1}{|y|.\sqrt[4]{ y }} \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y^{2}|}\\---------------\)
12. \(\dfrac{y^{\frac{1}{2}}}{y^{-1}}\\= y^{ \frac{1}{2} - (-1) }= y^{\frac{3}{2}}\\= \sqrt{ y^{3} } =|y|. \sqrt{ y } \\---------------\)