Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-5}{3}}}{a^{\frac{1}{2}}}\\= a^{ \frac{-5}{3} - \frac{1}{2} }= a^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ a^{13} }}\\=\frac{1}{|a^{2}|.\sqrt[6]{ a }}=\frac{1}{|a^{2}|.\sqrt[6]{ a }} \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a^{3}|}\\---------------\)
2. \(\dfrac{x^{\frac{-3}{4}}}{x^{\frac{5}{4}}}\\= x^{ \frac{-3}{4} - \frac{5}{4} }= x^{-2}\\=\frac{1}{x^{2}}\\---------------\)
3. \(\dfrac{q^{\frac{-1}{6}}}{q^{-1}}\\= q^{ \frac{-1}{6} - (-1) }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
4. \(\dfrac{x^{-1}}{x^{\frac{-1}{2}}}\\= x^{ -1 - (\frac{-1}{2}) }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
5. \(\dfrac{y^{\frac{1}{4}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{1}{4} - (\frac{-1}{2}) }= y^{\frac{3}{4}}\\=\sqrt[4]{ y^{3} }\\---------------\)
6. \(\dfrac{x^{\frac{-1}{6}}}{x^{\frac{2}{3}}}\\= x^{ \frac{-1}{6} - \frac{2}{3} }= x^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ x^{5} }}=\frac{1}{\sqrt[6]{ x^{5} }}. \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x|}\\---------------\)
7. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{-1}{2} - (\frac{-1}{2}) }= x^{0}\\=1\\---------------\)
8. \(\dfrac{y^{\frac{-5}{2}}}{y^{\frac{-4}{3}}}\\= y^{ \frac{-5}{2} - (\frac{-4}{3}) }= y^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[6]{ y }}=\frac{1}{|y|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{2}|}\\---------------\)
9. \(\dfrac{y^{\frac{-5}{2}}}{y^{\frac{1}{2}}}\\= y^{ \frac{-5}{2} - \frac{1}{2} }= y^{-3}\\=\frac{1}{y^{3}}\\---------------\)
10. \(\dfrac{a^{\frac{5}{6}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{5}{6} - (\frac{-2}{3}) }= a^{\frac{3}{2}}\\= \sqrt{ a^{3} } =|a|. \sqrt{ a } \\---------------\)
11. \(\dfrac{y^{\frac{-5}{3}}}{y^{\frac{-5}{4}}}\\= y^{ \frac{-5}{3} - (\frac{-5}{4}) }= y^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ y^{5} }}=\frac{1}{\sqrt[12]{ y^{5} }}. \color{purple}{\frac{\sqrt[12]{ y^{7} }}{\sqrt[12]{ y^{7} }}} \\=\frac{\sqrt[12]{ y^{7} }}{|y|}\\---------------\)
12. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{-2}{3} - (\frac{-1}{2}) }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)