Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{-1}{4}}}\\= q^{ \frac{-2}{3} - (\frac{-1}{4}) }= q^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ q^{5} }}=\frac{1}{\sqrt[12]{ q^{5} }}. \color{purple}{\frac{\sqrt[12]{ q^{7} }}{\sqrt[12]{ q^{7} }}} \\=\frac{\sqrt[12]{ q^{7} }}{|q|}\\---------------\)
2. \(\dfrac{q^{\frac{3}{2}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{3}{2} - (\frac{-1}{2}) }= q^{2}\\\\---------------\)
3. \(\dfrac{y^{\frac{5}{2}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{5}{2} - (\frac{-1}{3}) }= y^{\frac{17}{6}}\\=\sqrt[6]{ y^{17} }=|y^{2}|.\sqrt[6]{ y^{5} }\\---------------\)
4. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{5}{4}}}\\= y^{ \frac{2}{3} - \frac{5}{4} }= y^{\frac{-7}{12}}\\=\frac{1}{\sqrt[12]{ y^{7} }}=\frac{1}{\sqrt[12]{ y^{7} }}. \color{purple}{\frac{\sqrt[12]{ y^{5} }}{\sqrt[12]{ y^{5} }}} \\=\frac{\sqrt[12]{ y^{5} }}{|y|}\\---------------\)
5. \(\dfrac{q^{\frac{5}{3}}}{q^{\frac{3}{4}}}\\= q^{ \frac{5}{3} - \frac{3}{4} }= q^{\frac{11}{12}}\\=\sqrt[12]{ q^{11} }\\---------------\)
6. \(\dfrac{y^{\frac{-4}{5}}}{y^{\frac{5}{6}}}\\= y^{ \frac{-4}{5} - \frac{5}{6} }= y^{\frac{-49}{30}}\\=\frac{1}{\sqrt[30]{ y^{49} }}\\=\frac{1}{|y|.\sqrt[30]{ y^{19} }}=\frac{1}{|y|.\sqrt[30]{ y^{19} }} \color{purple}{\frac{\sqrt[30]{ y^{11} }}{\sqrt[30]{ y^{11} }}} \\=\frac{\sqrt[30]{ y^{11} }}{|y^{2}|}\\---------------\)
7. \(\dfrac{x^{\frac{-5}{2}}}{x^{\frac{1}{3}}}\\= x^{ \frac{-5}{2} - \frac{1}{3} }= x^{\frac{-17}{6}}\\=\frac{1}{\sqrt[6]{ x^{17} }}\\=\frac{1}{|x^{2}|.\sqrt[6]{ x^{5} }}=\frac{1}{|x^{2}|.\sqrt[6]{ x^{5} }} \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x^{3}|}\\---------------\)
8. \(\dfrac{y^{\frac{2}{5}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{2}{5} - (\frac{-1}{3}) }= y^{\frac{11}{15}}\\=\sqrt[15]{ y^{11} }\\---------------\)
9. \(\dfrac{y^{\frac{3}{4}}}{y^{1}}\\= y^{ \frac{3}{4} - 1 }= y^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ y }}=\frac{1}{\sqrt[4]{ y }}. \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y|}\\---------------\)
10. \(\dfrac{q^{\frac{-1}{3}}}{q^{1}}\\= q^{ \frac{-1}{3} - 1 }= q^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ q^{4} }}\\=\frac{1}{q.\sqrt[3]{ q }}=\frac{1}{q.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{2}}\\---------------\)
11. \(\dfrac{x^{\frac{-5}{4}}}{x^{\frac{-4}{5}}}\\= x^{ \frac{-5}{4} - (\frac{-4}{5}) }= x^{\frac{-9}{20}}\\=\frac{1}{\sqrt[20]{ x^{9} }}=\frac{1}{\sqrt[20]{ x^{9} }}. \color{purple}{\frac{\sqrt[20]{ x^{11} }}{\sqrt[20]{ x^{11} }}} \\=\frac{\sqrt[20]{ x^{11} }}{|x|}\\---------------\)
12. \(\dfrac{y^{-1}}{y^{-1}}\\= y^{ -1 - (-1) }= y^{0}\\=1\\---------------\)