Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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