Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{3}{5}}}\\= y^{ \frac{2}{3} - \frac{3}{5} }= y^{\frac{1}{15}}\\=\sqrt[15]{ y }\\---------------\)
2. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{5}{3}}}\\= a^{ \frac{-1}{2} - \frac{5}{3} }= a^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ a^{13} }}\\=\frac{1}{|a^{2}|.\sqrt[6]{ a }}=\frac{1}{|a^{2}|.\sqrt[6]{ a }} \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a^{3}|}\\---------------\)
3. \(\dfrac{y^{\frac{-2}{5}}}{y^{\frac{3}{2}}}\\= y^{ \frac{-2}{5} - \frac{3}{2} }= y^{\frac{-19}{10}}\\=\frac{1}{\sqrt[10]{ y^{19} }}\\=\frac{1}{|y|.\sqrt[10]{ y^{9} }}=\frac{1}{|y|.\sqrt[10]{ y^{9} }} \color{purple}{\frac{\sqrt[10]{ y }}{\sqrt[10]{ y }}} \\=\frac{\sqrt[10]{ y }}{|y^{2}|}\\---------------\)
4. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{1}{3}}}\\= y^{ \frac{-1}{3} - \frac{1}{3} }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
5. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{-5}{3}}}\\= q^{ \frac{-1}{2} - (\frac{-5}{3}) }= q^{\frac{7}{6}}\\=\sqrt[6]{ q^{7} }=|q|.\sqrt[6]{ q }\\---------------\)
6. \(\dfrac{q^{-1}}{q^{\frac{1}{5}}}\\= q^{ -1 - \frac{1}{5} }= q^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ q^{6} }}\\=\frac{1}{q.\sqrt[5]{ q }}=\frac{1}{q.\sqrt[5]{ q }} \color{purple}{\frac{\sqrt[5]{ q^{4} }}{\sqrt[5]{ q^{4} }}} \\=\frac{\sqrt[5]{ q^{4} }}{q^{2}}\\---------------\)
7. \(\dfrac{a^{\frac{5}{4}}}{a^{\frac{1}{3}}}\\= a^{ \frac{5}{4} - \frac{1}{3} }= a^{\frac{11}{12}}\\=\sqrt[12]{ a^{11} }\\---------------\)
8. \(\dfrac{y^{1}}{y^{\frac{-2}{5}}}\\= y^{ 1 - (\frac{-2}{5}) }= y^{\frac{7}{5}}\\=\sqrt[5]{ y^{7} }=y.\sqrt[5]{ y^{2} }\\---------------\)
9. \(\dfrac{a^{\frac{-5}{3}}}{a^{\frac{1}{6}}}\\= a^{ \frac{-5}{3} - \frac{1}{6} }= a^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ a^{11} }}\\=\frac{1}{|a|.\sqrt[6]{ a^{5} }}=\frac{1}{|a|.\sqrt[6]{ a^{5} }} \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a^{2}|}\\---------------\)
10. \(\dfrac{a^{\frac{-5}{2}}}{a^{1}}\\= a^{ \frac{-5}{2} - 1 }= a^{\frac{-7}{2}}\\=\frac{1}{ \sqrt{ a^{7} } }\\=\frac{1}{|a^{3}|. \sqrt{ a } }=\frac{1}{|a^{3}|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{4}|}\\---------------\)
11. \(\dfrac{y^{\frac{-1}{6}}}{y^{\frac{1}{6}}}\\= y^{ \frac{-1}{6} - \frac{1}{6} }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
12. \(\dfrac{x^{\frac{-4}{3}}}{x^{\frac{-5}{4}}}\\= x^{ \frac{-4}{3} - (\frac{-5}{4}) }= x^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ x }}=\frac{1}{\sqrt[12]{ x }}. \color{purple}{\frac{\sqrt[12]{ x^{11} }}{\sqrt[12]{ x^{11} }}} \\=\frac{\sqrt[12]{ x^{11} }}{|x|}\\---------------\)