Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{-1}{6}}}\\= y^{ \frac{-1}{3} - (\frac{-1}{6}) }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
2. \(\dfrac{y^{\frac{1}{3}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{1}{3} - (\frac{-1}{3}) }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
3. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{5}{3}}}\\= y^{ \frac{-1}{2} - \frac{5}{3} }= y^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ y^{13} }}\\=\frac{1}{|y^{2}|.\sqrt[6]{ y }}=\frac{1}{|y^{2}|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{3}|}\\---------------\)
4. \(\dfrac{q^{\frac{1}{4}}}{q^{\frac{5}{3}}}\\= q^{ \frac{1}{4} - \frac{5}{3} }= q^{\frac{-17}{12}}\\=\frac{1}{\sqrt[12]{ q^{17} }}\\=\frac{1}{|q|.\sqrt[12]{ q^{5} }}=\frac{1}{|q|.\sqrt[12]{ q^{5} }} \color{purple}{\frac{\sqrt[12]{ q^{7} }}{\sqrt[12]{ q^{7} }}} \\=\frac{\sqrt[12]{ q^{7} }}{|q^{2}|}\\---------------\)
5. \(\dfrac{y^{\frac{-4}{3}}}{y^{\frac{5}{4}}}\\= y^{ \frac{-4}{3} - \frac{5}{4} }= y^{\frac{-31}{12}}\\=\frac{1}{\sqrt[12]{ y^{31} }}\\=\frac{1}{|y^{2}|.\sqrt[12]{ y^{7} }}=\frac{1}{|y^{2}|.\sqrt[12]{ y^{7} }} \color{purple}{\frac{\sqrt[12]{ y^{5} }}{\sqrt[12]{ y^{5} }}} \\=\frac{\sqrt[12]{ y^{5} }}{|y^{3}|}\\---------------\)
6. \(\dfrac{x^{\frac{5}{2}}}{x^{\frac{-2}{3}}}\\= x^{ \frac{5}{2} - (\frac{-2}{3}) }= x^{\frac{19}{6}}\\=\sqrt[6]{ x^{19} }=|x^{3}|.\sqrt[6]{ x }\\---------------\)
7. \(\dfrac{a^{-2}}{a^{2}}\\= a^{ -2 - 2 }= a^{-4}\\=\frac{1}{a^{4}}\\---------------\)
8. \(\dfrac{y^{\frac{-2}{5}}}{y^{\frac{5}{3}}}\\= y^{ \frac{-2}{5} - \frac{5}{3} }= y^{\frac{-31}{15}}\\=\frac{1}{\sqrt[15]{ y^{31} }}\\=\frac{1}{y^{2}.\sqrt[15]{ y }}=\frac{1}{y^{2}.\sqrt[15]{ y }} \color{purple}{\frac{\sqrt[15]{ y^{14} }}{\sqrt[15]{ y^{14} }}} \\=\frac{\sqrt[15]{ y^{14} }}{y^{3}}\\---------------\)
9. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{4}{3}}}\\= q^{ \frac{-1}{2} - \frac{4}{3} }= q^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ q^{11} }}\\=\frac{1}{|q|.\sqrt[6]{ q^{5} }}=\frac{1}{|q|.\sqrt[6]{ q^{5} }} \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q^{2}|}\\---------------\)
10. \(\dfrac{y^{\frac{-5}{3}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{-5}{3} - (\frac{-1}{2}) }= y^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[6]{ y }}=\frac{1}{|y|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{2}|}\\---------------\)
11. \(\dfrac{q^{\frac{1}{6}}}{q^{\frac{3}{2}}}\\= q^{ \frac{1}{6} - \frac{3}{2} }= q^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ q^{4} }}\\=\frac{1}{q.\sqrt[3]{ q }}=\frac{1}{q.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{2}}\\---------------\)
12. \(\dfrac{y^{1}}{y^{\frac{1}{4}}}\\= y^{ 1 - \frac{1}{4} }= y^{\frac{3}{4}}\\=\sqrt[4]{ y^{3} }\\---------------\)