Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{-1}{2} - (\frac{-1}{2}) }= y^{0}\\=1\\---------------\)
2. \(\dfrac{y^{\frac{4}{5}}}{y^{\frac{1}{2}}}\\= y^{ \frac{4}{5} - \frac{1}{2} }= y^{\frac{3}{10}}\\=\sqrt[10]{ y^{3} }\\---------------\)
3. \(\dfrac{a^{\frac{-5}{3}}}{a^{\frac{3}{2}}}\\= a^{ \frac{-5}{3} - \frac{3}{2} }= a^{\frac{-19}{6}}\\=\frac{1}{\sqrt[6]{ a^{19} }}\\=\frac{1}{|a^{3}|.\sqrt[6]{ a }}=\frac{1}{|a^{3}|.\sqrt[6]{ a }} \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a^{4}|}\\---------------\)
4. \(\dfrac{x^{\frac{2}{5}}}{x^{\frac{1}{2}}}\\= x^{ \frac{2}{5} - \frac{1}{2} }= x^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ x }}=\frac{1}{\sqrt[10]{ x }}. \color{purple}{\frac{\sqrt[10]{ x^{9} }}{\sqrt[10]{ x^{9} }}} \\=\frac{\sqrt[10]{ x^{9} }}{|x|}\\---------------\)
5. \(\dfrac{a^{\frac{-1}{5}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{-1}{5} - (\frac{-1}{3}) }= a^{\frac{2}{15}}\\=\sqrt[15]{ a^{2} }\\---------------\)
6. \(\dfrac{y^{\frac{5}{2}}}{y^{\frac{-2}{5}}}\\= y^{ \frac{5}{2} - (\frac{-2}{5}) }= y^{\frac{29}{10}}\\=\sqrt[10]{ y^{29} }=|y^{2}|.\sqrt[10]{ y^{9} }\\---------------\)
7. \(\dfrac{y^{\frac{-5}{4}}}{y^{-1}}\\= y^{ \frac{-5}{4} - (-1) }= y^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ y }}=\frac{1}{\sqrt[4]{ y }}. \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y|}\\---------------\)
8. \(\dfrac{x^{\frac{-5}{6}}}{x^{\frac{-4}{5}}}\\= x^{ \frac{-5}{6} - (\frac{-4}{5}) }= x^{\frac{-1}{30}}\\=\frac{1}{\sqrt[30]{ x }}=\frac{1}{\sqrt[30]{ x }}. \color{purple}{\frac{\sqrt[30]{ x^{29} }}{\sqrt[30]{ x^{29} }}} \\=\frac{\sqrt[30]{ x^{29} }}{|x|}\\---------------\)
9. \(\dfrac{a^{\frac{1}{5}}}{a^{\frac{2}{3}}}\\= a^{ \frac{1}{5} - \frac{2}{3} }= a^{\frac{-7}{15}}\\=\frac{1}{\sqrt[15]{ a^{7} }}=\frac{1}{\sqrt[15]{ a^{7} }}. \color{purple}{\frac{\sqrt[15]{ a^{8} }}{\sqrt[15]{ a^{8} }}} \\=\frac{\sqrt[15]{ a^{8} }}{a}\\---------------\)
10. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{1}{5}}}\\= q^{ \frac{-1}{2} - \frac{1}{5} }= q^{\frac{-7}{10}}\\=\frac{1}{\sqrt[10]{ q^{7} }}=\frac{1}{\sqrt[10]{ q^{7} }}. \color{purple}{\frac{\sqrt[10]{ q^{3} }}{\sqrt[10]{ q^{3} }}} \\=\frac{\sqrt[10]{ q^{3} }}{|q|}\\---------------\)
11. \(\dfrac{a^{\frac{3}{4}}}{a^{\frac{-3}{4}}}\\= a^{ \frac{3}{4} - (\frac{-3}{4}) }= a^{\frac{3}{2}}\\= \sqrt{ a^{3} } =|a|. \sqrt{ a } \\---------------\)
12. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{2}{3} - (\frac{-1}{2}) }= y^{\frac{7}{6}}\\=\sqrt[6]{ y^{7} }=|y|.\sqrt[6]{ y }\\---------------\)