Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{4}{5}}}\\= a^{ \frac{-1}{3} - \frac{4}{5} }= a^{\frac{-17}{15}}\\=\frac{1}{\sqrt[15]{ a^{17} }}\\=\frac{1}{a.\sqrt[15]{ a^{2} }}=\frac{1}{a.\sqrt[15]{ a^{2} }} \color{purple}{\frac{\sqrt[15]{ a^{13} }}{\sqrt[15]{ a^{13} }}} \\=\frac{\sqrt[15]{ a^{13} }}{a^{2}}\\---------------\)
2. \(\dfrac{a^{\frac{-1}{2}}}{a^{1}}\\= a^{ \frac{-1}{2} - 1 }= a^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ a^{3} } }\\=\frac{1}{|a|. \sqrt{ a } }=\frac{1}{|a|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{2}|}\\---------------\)
3. \(\dfrac{y^{-1}}{y^{\frac{2}{5}}}\\= y^{ -1 - \frac{2}{5} }= y^{\frac{-7}{5}}\\=\frac{1}{\sqrt[5]{ y^{7} }}\\=\frac{1}{y.\sqrt[5]{ y^{2} }}=\frac{1}{y.\sqrt[5]{ y^{2} }} \color{purple}{\frac{\sqrt[5]{ y^{3} }}{\sqrt[5]{ y^{3} }}} \\=\frac{\sqrt[5]{ y^{3} }}{y^{2}}\\---------------\)
4. \(\dfrac{q^{\frac{-2}{5}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{-2}{5} - (\frac{-1}{3}) }= q^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ q }}=\frac{1}{\sqrt[15]{ q }}. \color{purple}{\frac{\sqrt[15]{ q^{14} }}{\sqrt[15]{ q^{14} }}} \\=\frac{\sqrt[15]{ q^{14} }}{q}\\---------------\)
5. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{5}{4}}}\\= q^{ \frac{1}{2} - \frac{5}{4} }= q^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ q^{3} }}=\frac{1}{\sqrt[4]{ q^{3} }}. \color{purple}{\frac{\sqrt[4]{ q }}{\sqrt[4]{ q }}} \\=\frac{\sqrt[4]{ q }}{|q|}\\---------------\)
6. \(\dfrac{q^{\frac{5}{3}}}{q^{\frac{5}{2}}}\\= q^{ \frac{5}{3} - \frac{5}{2} }= q^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ q^{5} }}=\frac{1}{\sqrt[6]{ q^{5} }}. \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q|}\\---------------\)
7. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{-4}{3}}}\\= a^{ \frac{-1}{2} - (\frac{-4}{3}) }= a^{\frac{5}{6}}\\=\sqrt[6]{ a^{5} }\\---------------\)
8. \(\dfrac{q^{\frac{-1}{3}}}{q^{-1}}\\= q^{ \frac{-1}{3} - (-1) }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
9. \(\dfrac{y^{\frac{-1}{4}}}{y^{\frac{2}{5}}}\\= y^{ \frac{-1}{4} - \frac{2}{5} }= y^{\frac{-13}{20}}\\=\frac{1}{\sqrt[20]{ y^{13} }}=\frac{1}{\sqrt[20]{ y^{13} }}. \color{purple}{\frac{\sqrt[20]{ y^{7} }}{\sqrt[20]{ y^{7} }}} \\=\frac{\sqrt[20]{ y^{7} }}{|y|}\\---------------\)
10. \(\dfrac{x^{\frac{5}{2}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{5}{2} - (\frac{-1}{2}) }= x^{3}\\\\---------------\)
11. \(\dfrac{x^{-2}}{x^{\frac{2}{5}}}\\= x^{ -2 - \frac{2}{5} }= x^{\frac{-12}{5}}\\=\frac{1}{\sqrt[5]{ x^{12} }}\\=\frac{1}{x^{2}.\sqrt[5]{ x^{2} }}=\frac{1}{x^{2}.\sqrt[5]{ x^{2} }} \color{purple}{\frac{\sqrt[5]{ x^{3} }}{\sqrt[5]{ x^{3} }}} \\=\frac{\sqrt[5]{ x^{3} }}{x^{3}}\\---------------\)
12. \(\dfrac{x^{\frac{4}{5}}}{x^{\frac{1}{3}}}\\= x^{ \frac{4}{5} - \frac{1}{3} }= x^{\frac{7}{15}}\\=\sqrt[15]{ x^{7} }\\---------------\)