Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{-1}}{x^{\frac{1}{2}}}\\= x^{ -1 - \frac{1}{2} }= x^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ x^{3} } }\\=\frac{1}{|x|. \sqrt{ x } }=\frac{1}{|x|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{2}|}\\---------------\)
2. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{3}{4}}}\\= y^{ \frac{-2}{3} - \frac{3}{4} }= y^{\frac{-17}{12}}\\=\frac{1}{\sqrt[12]{ y^{17} }}\\=\frac{1}{|y|.\sqrt[12]{ y^{5} }}=\frac{1}{|y|.\sqrt[12]{ y^{5} }} \color{purple}{\frac{\sqrt[12]{ y^{7} }}{\sqrt[12]{ y^{7} }}} \\=\frac{\sqrt[12]{ y^{7} }}{|y^{2}|}\\---------------\)
3. \(\dfrac{y^{\frac{3}{4}}}{y^{1}}\\= y^{ \frac{3}{4} - 1 }= y^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ y }}=\frac{1}{\sqrt[4]{ y }}. \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y|}\\---------------\)
4. \(\dfrac{y^{\frac{-5}{2}}}{y^{\frac{-4}{5}}}\\= y^{ \frac{-5}{2} - (\frac{-4}{5}) }= y^{\frac{-17}{10}}\\=\frac{1}{\sqrt[10]{ y^{17} }}\\=\frac{1}{|y|.\sqrt[10]{ y^{7} }}=\frac{1}{|y|.\sqrt[10]{ y^{7} }} \color{purple}{\frac{\sqrt[10]{ y^{3} }}{\sqrt[10]{ y^{3} }}} \\=\frac{\sqrt[10]{ y^{3} }}{|y^{2}|}\\---------------\)
5. \(\dfrac{q^{\frac{-5}{4}}}{q^{\frac{3}{4}}}\\= q^{ \frac{-5}{4} - \frac{3}{4} }= q^{-2}\\=\frac{1}{q^{2}}\\---------------\)
6. \(\dfrac{y^{1}}{y^{\frac{2}{3}}}\\= y^{ 1 - \frac{2}{3} }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
7. \(\dfrac{q^{\frac{-1}{6}}}{q^{-1}}\\= q^{ \frac{-1}{6} - (-1) }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
8. \(\dfrac{a^{\frac{5}{4}}}{a^{\frac{4}{3}}}\\= a^{ \frac{5}{4} - \frac{4}{3} }= a^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ a }}=\frac{1}{\sqrt[12]{ a }}. \color{purple}{\frac{\sqrt[12]{ a^{11} }}{\sqrt[12]{ a^{11} }}} \\=\frac{\sqrt[12]{ a^{11} }}{|a|}\\---------------\)
9. \(\dfrac{a^{1}}{a^{\frac{4}{3}}}\\= a^{ 1 - \frac{4}{3} }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
10. \(\dfrac{x^{\frac{1}{5}}}{x^{\frac{5}{6}}}\\= x^{ \frac{1}{5} - \frac{5}{6} }= x^{\frac{-19}{30}}\\=\frac{1}{\sqrt[30]{ x^{19} }}=\frac{1}{\sqrt[30]{ x^{19} }}. \color{purple}{\frac{\sqrt[30]{ x^{11} }}{\sqrt[30]{ x^{11} }}} \\=\frac{\sqrt[30]{ x^{11} }}{|x|}\\---------------\)
11. \(\dfrac{x^{1}}{x^{\frac{-4}{5}}}\\= x^{ 1 - (\frac{-4}{5}) }= x^{\frac{9}{5}}\\=\sqrt[5]{ x^{9} }=x.\sqrt[5]{ x^{4} }\\---------------\)
12. \(\dfrac{y^{1}}{y^{\frac{-2}{3}}}\\= y^{ 1 - (\frac{-2}{3}) }= y^{\frac{5}{3}}\\=\sqrt[3]{ y^{5} }=y.\sqrt[3]{ y^{2} }\\---------------\)