Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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