Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{1}{4}}}\\= q^{ \frac{1}{2} - \frac{1}{4} }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
2. \(\dfrac{q^{2}}{q^{\frac{5}{2}}}\\= q^{ 2 - \frac{5}{2} }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
3. \(\dfrac{q^{\frac{1}{4}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{1}{4} - (\frac{-1}{2}) }= q^{\frac{3}{4}}\\=\sqrt[4]{ q^{3} }\\---------------\)
4. \(\dfrac{x^{\frac{2}{5}}}{x^{\frac{-5}{2}}}\\= x^{ \frac{2}{5} - (\frac{-5}{2}) }= x^{\frac{29}{10}}\\=\sqrt[10]{ x^{29} }=|x^{2}|.\sqrt[10]{ x^{9} }\\---------------\)
5. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{-1}{5}}}\\= x^{ \frac{-1}{2} - (\frac{-1}{5}) }= x^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ x^{3} }}=\frac{1}{\sqrt[10]{ x^{3} }}. \color{purple}{\frac{\sqrt[10]{ x^{7} }}{\sqrt[10]{ x^{7} }}} \\=\frac{\sqrt[10]{ x^{7} }}{|x|}\\---------------\)
6. \(\dfrac{a^{1}}{a^{\frac{2}{5}}}\\= a^{ 1 - \frac{2}{5} }= a^{\frac{3}{5}}\\=\sqrt[5]{ a^{3} }\\---------------\)
7. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{-2}{3}}}\\= x^{ \frac{-1}{3} - (\frac{-2}{3}) }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
8. \(\dfrac{x^{2}}{x^{\frac{-2}{5}}}\\= x^{ 2 - (\frac{-2}{5}) }= x^{\frac{12}{5}}\\=\sqrt[5]{ x^{12} }=x^{2}.\sqrt[5]{ x^{2} }\\---------------\)
9. \(\dfrac{x^{\frac{-4}{3}}}{x^{\frac{1}{5}}}\\= x^{ \frac{-4}{3} - \frac{1}{5} }= x^{\frac{-23}{15}}\\=\frac{1}{\sqrt[15]{ x^{23} }}\\=\frac{1}{x.\sqrt[15]{ x^{8} }}=\frac{1}{x.\sqrt[15]{ x^{8} }} \color{purple}{\frac{\sqrt[15]{ x^{7} }}{\sqrt[15]{ x^{7} }}} \\=\frac{\sqrt[15]{ x^{7} }}{x^{2}}\\---------------\)
10. \(\dfrac{y^{\frac{3}{5}}}{y^{\frac{3}{2}}}\\= y^{ \frac{3}{5} - \frac{3}{2} }= y^{\frac{-9}{10}}\\=\frac{1}{\sqrt[10]{ y^{9} }}=\frac{1}{\sqrt[10]{ y^{9} }}. \color{purple}{\frac{\sqrt[10]{ y }}{\sqrt[10]{ y }}} \\=\frac{\sqrt[10]{ y }}{|y|}\\---------------\)
11. \(\dfrac{a^{\frac{-1}{4}}}{a^{\frac{3}{2}}}\\= a^{ \frac{-1}{4} - \frac{3}{2} }= a^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ a^{7} }}\\=\frac{1}{|a|.\sqrt[4]{ a^{3} }}=\frac{1}{|a|.\sqrt[4]{ a^{3} }} \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a^{2}|}\\---------------\)
12. \(\dfrac{y^{\frac{-1}{4}}}{y^{\frac{-1}{6}}}\\= y^{ \frac{-1}{4} - (\frac{-1}{6}) }= y^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ y }}=\frac{1}{\sqrt[12]{ y }}. \color{purple}{\frac{\sqrt[12]{ y^{11} }}{\sqrt[12]{ y^{11} }}} \\=\frac{\sqrt[12]{ y^{11} }}{|y|}\\---------------\)