Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{3}{4}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{3}{4} - (\frac{-1}{3}) }= y^{\frac{13}{12}}\\=\sqrt[12]{ y^{13} }=|y|.\sqrt[12]{ y }\\---------------\)
2. \(\dfrac{x^{\frac{4}{3}}}{x^{\frac{3}{5}}}\\= x^{ \frac{4}{3} - \frac{3}{5} }= x^{\frac{11}{15}}\\=\sqrt[15]{ x^{11} }\\---------------\)
3. \(\dfrac{a^{\frac{4}{3}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{4}{3} - (\frac{-2}{3}) }= a^{2}\\\\---------------\)
4. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{-4}{3}}}\\= y^{ \frac{-1}{2} - (\frac{-4}{3}) }= y^{\frac{5}{6}}\\=\sqrt[6]{ y^{5} }\\---------------\)
5. \(\dfrac{q^{\frac{3}{4}}}{q^{\frac{5}{3}}}\\= q^{ \frac{3}{4} - \frac{5}{3} }= q^{\frac{-11}{12}}\\=\frac{1}{\sqrt[12]{ q^{11} }}=\frac{1}{\sqrt[12]{ q^{11} }}. \color{purple}{\frac{\sqrt[12]{ q }}{\sqrt[12]{ q }}} \\=\frac{\sqrt[12]{ q }}{|q|}\\---------------\)
6. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{-2}{5}}}\\= q^{ \frac{2}{3} - (\frac{-2}{5}) }= q^{\frac{16}{15}}\\=\sqrt[15]{ q^{16} }=q.\sqrt[15]{ q }\\---------------\)
7. \(\dfrac{q^{\frac{-5}{4}}}{q^{\frac{1}{2}}}\\= q^{ \frac{-5}{4} - \frac{1}{2} }= q^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ q^{7} }}\\=\frac{1}{|q|.\sqrt[4]{ q^{3} }}=\frac{1}{|q|.\sqrt[4]{ q^{3} }} \color{purple}{\frac{\sqrt[4]{ q }}{\sqrt[4]{ q }}} \\=\frac{\sqrt[4]{ q }}{|q^{2}|}\\---------------\)
8. \(\dfrac{y^{\frac{1}{4}}}{y^{-1}}\\= y^{ \frac{1}{4} - (-1) }= y^{\frac{5}{4}}\\=\sqrt[4]{ y^{5} }=|y|.\sqrt[4]{ y }\\---------------\)
9. \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{2}{3}}}\\= x^{ \frac{-2}{3} - \frac{2}{3} }= x^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ x^{4} }}\\=\frac{1}{x.\sqrt[3]{ x }}=\frac{1}{x.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{2}}\\---------------\)
10. \(\dfrac{y^{-1}}{y^{\frac{5}{6}}}\\= y^{ -1 - \frac{5}{6} }= y^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ y^{11} }}\\=\frac{1}{|y|.\sqrt[6]{ y^{5} }}=\frac{1}{|y|.\sqrt[6]{ y^{5} }} \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y^{2}|}\\---------------\)
11. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{3}{2}}}\\= y^{ \frac{-1}{2} - \frac{3}{2} }= y^{-2}\\=\frac{1}{y^{2}}\\---------------\)
12. \(\dfrac{x^{\frac{-2}{5}}}{x^{\frac{2}{3}}}\\= x^{ \frac{-2}{5} - \frac{2}{3} }= x^{\frac{-16}{15}}\\=\frac{1}{\sqrt[15]{ x^{16} }}\\=\frac{1}{x.\sqrt[15]{ x }}=\frac{1}{x.\sqrt[15]{ x }} \color{purple}{\frac{\sqrt[15]{ x^{14} }}{\sqrt[15]{ x^{14} }}} \\=\frac{\sqrt[15]{ x^{14} }}{x^{2}}\\---------------\)