Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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