Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-5}{3}}}{a^{\frac{-1}{6}}}\\= a^{ \frac{-5}{3} - (\frac{-1}{6}) }= a^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ a^{3} } }\\=\frac{1}{|a|. \sqrt{ a } }=\frac{1}{|a|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{2}|}\\---------------\)
2. \(\dfrac{y^{\frac{1}{4}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{1}{4} - (\frac{-1}{3}) }= y^{\frac{7}{12}}\\=\sqrt[12]{ y^{7} }\\---------------\)
3. \(\dfrac{x^{\frac{-5}{4}}}{x^{\frac{-1}{4}}}\\= x^{ \frac{-5}{4} - (\frac{-1}{4}) }= x^{-1}\\=\frac{1}{x}\\---------------\)
4. \(\dfrac{y^{\frac{2}{3}}}{y^{1}}\\= y^{ \frac{2}{3} - 1 }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
5. \(\dfrac{y^{-1}}{y^{\frac{-5}{6}}}\\= y^{ -1 - (\frac{-5}{6}) }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
6. \(\dfrac{y^{\frac{1}{3}}}{y^{-1}}\\= y^{ \frac{1}{3} - (-1) }= y^{\frac{4}{3}}\\=\sqrt[3]{ y^{4} }=y.\sqrt[3]{ y }\\---------------\)
7. \(\dfrac{x^{\frac{-1}{4}}}{x^{\frac{3}{4}}}\\= x^{ \frac{-1}{4} - \frac{3}{4} }= x^{-1}\\=\frac{1}{x}\\---------------\)
8. \(\dfrac{y^{\frac{3}{2}}}{y^{-1}}\\= y^{ \frac{3}{2} - (-1) }= y^{\frac{5}{2}}\\= \sqrt{ y^{5} } =|y^{2}|. \sqrt{ y } \\---------------\)
9. \(\dfrac{y^{\frac{1}{2}}}{y^{-1}}\\= y^{ \frac{1}{2} - (-1) }= y^{\frac{3}{2}}\\= \sqrt{ y^{3} } =|y|. \sqrt{ y } \\---------------\)
10. \(\dfrac{x^{\frac{-2}{5}}}{x^{-1}}\\= x^{ \frac{-2}{5} - (-1) }= x^{\frac{3}{5}}\\=\sqrt[5]{ x^{3} }\\---------------\)
11. \(\dfrac{q^{\frac{4}{5}}}{q^{\frac{1}{6}}}\\= q^{ \frac{4}{5} - \frac{1}{6} }= q^{\frac{19}{30}}\\=\sqrt[30]{ q^{19} }\\---------------\)
12. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{-3}{2}}}\\= y^{ \frac{1}{2} - (\frac{-3}{2}) }= y^{2}\\\\---------------\)