Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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