Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-3}{4}}}{q^{\frac{5}{4}}}\\= q^{ \frac{-3}{4} - \frac{5}{4} }= q^{-2}\\=\frac{1}{q^{2}}\\---------------\)
2. \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{3}{4}}}\\= x^{ \frac{-2}{3} - \frac{3}{4} }= x^{\frac{-17}{12}}\\=\frac{1}{\sqrt[12]{ x^{17} }}\\=\frac{1}{|x|.\sqrt[12]{ x^{5} }}=\frac{1}{|x|.\sqrt[12]{ x^{5} }} \color{purple}{\frac{\sqrt[12]{ x^{7} }}{\sqrt[12]{ x^{7} }}} \\=\frac{\sqrt[12]{ x^{7} }}{|x^{2}|}\\---------------\)
3. \(\dfrac{a^{\frac{-5}{4}}}{a^{\frac{1}{2}}}\\= a^{ \frac{-5}{4} - \frac{1}{2} }= a^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ a^{7} }}\\=\frac{1}{|a|.\sqrt[4]{ a^{3} }}=\frac{1}{|a|.\sqrt[4]{ a^{3} }} \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a^{2}|}\\---------------\)
4. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{2}{3} - (\frac{-1}{2}) }= x^{\frac{7}{6}}\\=\sqrt[6]{ x^{7} }=|x|.\sqrt[6]{ x }\\---------------\)
5. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{1}{4}}}\\= a^{ \frac{-1}{2} - \frac{1}{4} }= a^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ a^{3} }}=\frac{1}{\sqrt[4]{ a^{3} }}. \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a|}\\---------------\)
6. \(\dfrac{a^{1}}{a^{\frac{3}{2}}}\\= a^{ 1 - \frac{3}{2} }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
7. \(\dfrac{q^{\frac{1}{5}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{1}{5} - (\frac{-1}{2}) }= q^{\frac{7}{10}}\\=\sqrt[10]{ q^{7} }\\---------------\)
8. \(\dfrac{y^{\frac{-3}{5}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{-3}{5} - (\frac{-1}{3}) }= y^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ y^{4} }}=\frac{1}{\sqrt[15]{ y^{4} }}. \color{purple}{\frac{\sqrt[15]{ y^{11} }}{\sqrt[15]{ y^{11} }}} \\=\frac{\sqrt[15]{ y^{11} }}{y}\\---------------\)
9. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{1}{3} - (\frac{-1}{2}) }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
10. \(\dfrac{x^{\frac{4}{3}}}{x^{\frac{-5}{4}}}\\= x^{ \frac{4}{3} - (\frac{-5}{4}) }= x^{\frac{31}{12}}\\=\sqrt[12]{ x^{31} }=|x^{2}|.\sqrt[12]{ x^{7} }\\---------------\)
11. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{2}{3}}}\\= y^{ \frac{-1}{2} - \frac{2}{3} }= y^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[6]{ y }}=\frac{1}{|y|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{2}|}\\---------------\)
12. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{3}{5}}}\\= y^{ \frac{-1}{3} - \frac{3}{5} }= y^{\frac{-14}{15}}\\=\frac{1}{\sqrt[15]{ y^{14} }}=\frac{1}{\sqrt[15]{ y^{14} }}. \color{purple}{\frac{\sqrt[15]{ y }}{\sqrt[15]{ y }}} \\=\frac{\sqrt[15]{ y }}{y}\\---------------\)