Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{-3}{2}}}\\= x^{ \frac{-1}{3} - (\frac{-3}{2}) }= x^{\frac{7}{6}}\\=\sqrt[6]{ x^{7} }=|x|.\sqrt[6]{ x }\\---------------\)
2. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{2}{5}}}\\= a^{ \frac{-2}{3} - \frac{2}{5} }= a^{\frac{-16}{15}}\\=\frac{1}{\sqrt[15]{ a^{16} }}\\=\frac{1}{a.\sqrt[15]{ a }}=\frac{1}{a.\sqrt[15]{ a }} \color{purple}{\frac{\sqrt[15]{ a^{14} }}{\sqrt[15]{ a^{14} }}} \\=\frac{\sqrt[15]{ a^{14} }}{a^{2}}\\---------------\)
3. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{1}{6}}}\\= q^{ \frac{-2}{3} - \frac{1}{6} }= q^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ q^{5} }}=\frac{1}{\sqrt[6]{ q^{5} }}. \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q|}\\---------------\)
4. \(\dfrac{a^{1}}{a^{\frac{4}{5}}}\\= a^{ 1 - \frac{4}{5} }= a^{\frac{1}{5}}\\=\sqrt[5]{ a }\\---------------\)
5. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{1}{2}}}\\= q^{ \frac{2}{3} - \frac{1}{2} }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
6. \(\dfrac{y^{\frac{-1}{6}}}{y^{1}}\\= y^{ \frac{-1}{6} - 1 }= y^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[6]{ y }}=\frac{1}{|y|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{2}|}\\---------------\)
7. \(\dfrac{a^{\frac{-1}{3}}}{a^{-2}}\\= a^{ \frac{-1}{3} - (-2) }= a^{\frac{5}{3}}\\=\sqrt[3]{ a^{5} }=a.\sqrt[3]{ a^{2} }\\---------------\)
8. \(\dfrac{x^{\frac{-4}{5}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{-4}{5} - (\frac{-1}{3}) }= x^{\frac{-7}{15}}\\=\frac{1}{\sqrt[15]{ x^{7} }}=\frac{1}{\sqrt[15]{ x^{7} }}. \color{purple}{\frac{\sqrt[15]{ x^{8} }}{\sqrt[15]{ x^{8} }}} \\=\frac{\sqrt[15]{ x^{8} }}{x}\\---------------\)
9. \(\dfrac{x^{\frac{-5}{4}}}{x^{\frac{3}{4}}}\\= x^{ \frac{-5}{4} - \frac{3}{4} }= x^{-2}\\=\frac{1}{x^{2}}\\---------------\)
10. \(\dfrac{a^{\frac{4}{5}}}{a^{-1}}\\= a^{ \frac{4}{5} - (-1) }= a^{\frac{9}{5}}\\=\sqrt[5]{ a^{9} }=a.\sqrt[5]{ a^{4} }\\---------------\)
11. \(\dfrac{q^{\frac{1}{4}}}{q^{\frac{1}{4}}}\\= q^{ \frac{1}{4} - \frac{1}{4} }= q^{0}\\=1\\---------------\)
12. \(\dfrac{q^{\frac{-1}{4}}}{q^{\frac{5}{6}}}\\= q^{ \frac{-1}{4} - \frac{5}{6} }= q^{\frac{-13}{12}}\\=\frac{1}{\sqrt[12]{ q^{13} }}\\=\frac{1}{|q|.\sqrt[12]{ q }}=\frac{1}{|q|.\sqrt[12]{ q }} \color{purple}{\frac{\sqrt[12]{ q^{11} }}{\sqrt[12]{ q^{11} }}} \\=\frac{\sqrt[12]{ q^{11} }}{|q^{2}|}\\---------------\)