Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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