Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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