Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-5}{3}}}{a^{\frac{-1}{4}}}\\= a^{ \frac{-5}{3} - (\frac{-1}{4}) }= a^{\frac{-17}{12}}\\=\frac{1}{\sqrt[12]{ a^{17} }}\\=\frac{1}{|a|.\sqrt[12]{ a^{5} }}=\frac{1}{|a|.\sqrt[12]{ a^{5} }} \color{purple}{\frac{\sqrt[12]{ a^{7} }}{\sqrt[12]{ a^{7} }}} \\=\frac{\sqrt[12]{ a^{7} }}{|a^{2}|}\\---------------\)
2. \(\dfrac{a^{\frac{3}{5}}}{a^{\frac{4}{5}}}\\= a^{ \frac{3}{5} - \frac{4}{5} }= a^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ a }}=\frac{1}{\sqrt[5]{ a }}. \color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a}\\---------------\)
3. \(\dfrac{y^{\frac{1}{2}}}{y^{1}}\\= y^{ \frac{1}{2} - 1 }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
4. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{-3}{2}}}\\= y^{ \frac{1}{2} - (\frac{-3}{2}) }= y^{2}\\\\---------------\)
5. \(\dfrac{x^{\frac{-1}{5}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{-1}{5} - (\frac{-1}{2}) }= x^{\frac{3}{10}}\\=\sqrt[10]{ x^{3} }\\---------------\)
6. \(\dfrac{x^{\frac{5}{4}}}{x^{\frac{1}{5}}}\\= x^{ \frac{5}{4} - \frac{1}{5} }= x^{\frac{21}{20}}\\=\sqrt[20]{ x^{21} }=|x|.\sqrt[20]{ x }\\---------------\)
7. \(\dfrac{a^{1}}{a^{\frac{5}{6}}}\\= a^{ 1 - \frac{5}{6} }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)
8. \(\dfrac{x^{1}}{x^{\frac{-5}{2}}}\\= x^{ 1 - (\frac{-5}{2}) }= x^{\frac{7}{2}}\\= \sqrt{ x^{7} } =|x^{3}|. \sqrt{ x } \\---------------\)
9. \(\dfrac{y^{\frac{1}{3}}}{y^{\frac{5}{3}}}\\= y^{ \frac{1}{3} - \frac{5}{3} }= y^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ y^{4} }}\\=\frac{1}{y.\sqrt[3]{ y }}=\frac{1}{y.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{2}}\\---------------\)
10. \(\dfrac{x^{\frac{-4}{3}}}{x^{\frac{-5}{2}}}\\= x^{ \frac{-4}{3} - (\frac{-5}{2}) }= x^{\frac{7}{6}}\\=\sqrt[6]{ x^{7} }=|x|.\sqrt[6]{ x }\\---------------\)
11. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{-5}{6}}}\\= q^{ \frac{1}{2} - (\frac{-5}{6}) }= q^{\frac{4}{3}}\\=\sqrt[3]{ q^{4} }=q.\sqrt[3]{ q }\\---------------\)
12. \(\dfrac{y^{-1}}{y^{\frac{1}{2}}}\\= y^{ -1 - \frac{1}{2} }= y^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ y^{3} } }\\=\frac{1}{|y|. \sqrt{ y } }=\frac{1}{|y|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{2}|}\\---------------\)