Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{2}{5}}}\\= y^{ \frac{-2}{3} - \frac{2}{5} }= y^{\frac{-16}{15}}\\=\frac{1}{\sqrt[15]{ y^{16} }}\\=\frac{1}{y.\sqrt[15]{ y }}=\frac{1}{y.\sqrt[15]{ y }} \color{purple}{\frac{\sqrt[15]{ y^{14} }}{\sqrt[15]{ y^{14} }}} \\=\frac{\sqrt[15]{ y^{14} }}{y^{2}}\\---------------\)
2. \(\dfrac{a^{\frac{5}{6}}}{a^{\frac{5}{4}}}\\= a^{ \frac{5}{6} - \frac{5}{4} }= a^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ a^{5} }}=\frac{1}{\sqrt[12]{ a^{5} }}. \color{purple}{\frac{\sqrt[12]{ a^{7} }}{\sqrt[12]{ a^{7} }}} \\=\frac{\sqrt[12]{ a^{7} }}{|a|}\\---------------\)
3. \(\dfrac{q^{\frac{3}{5}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{3}{5} - (\frac{-2}{3}) }= q^{\frac{19}{15}}\\=\sqrt[15]{ q^{19} }=q.\sqrt[15]{ q^{4} }\\---------------\)
4. \(\dfrac{x^{\frac{-1}{6}}}{x^{-1}}\\= x^{ \frac{-1}{6} - (-1) }= x^{\frac{5}{6}}\\=\sqrt[6]{ x^{5} }\\---------------\)
5. \(\dfrac{a^{\frac{-4}{3}}}{a^{-1}}\\= a^{ \frac{-4}{3} - (-1) }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
6. \(\dfrac{q^{\frac{5}{2}}}{q^{\frac{2}{5}}}\\= q^{ \frac{5}{2} - \frac{2}{5} }= q^{\frac{21}{10}}\\=\sqrt[10]{ q^{21} }=|q^{2}|.\sqrt[10]{ q }\\---------------\)
7. \(\dfrac{q^{\frac{5}{4}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{5}{4} - (\frac{-1}{2}) }= q^{\frac{7}{4}}\\=\sqrt[4]{ q^{7} }=|q|.\sqrt[4]{ q^{3} }\\---------------\)
8. \(\dfrac{q^{\frac{-5}{6}}}{q^{\frac{-4}{5}}}\\= q^{ \frac{-5}{6} - (\frac{-4}{5}) }= q^{\frac{-1}{30}}\\=\frac{1}{\sqrt[30]{ q }}=\frac{1}{\sqrt[30]{ q }}. \color{purple}{\frac{\sqrt[30]{ q^{29} }}{\sqrt[30]{ q^{29} }}} \\=\frac{\sqrt[30]{ q^{29} }}{|q|}\\---------------\)
9. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{-2}{5}}}\\= a^{ \frac{-2}{3} - (\frac{-2}{5}) }= a^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ a^{4} }}=\frac{1}{\sqrt[15]{ a^{4} }}. \color{purple}{\frac{\sqrt[15]{ a^{11} }}{\sqrt[15]{ a^{11} }}} \\=\frac{\sqrt[15]{ a^{11} }}{a}\\---------------\)
10. \(\dfrac{q^{\frac{-5}{4}}}{q^{\frac{-3}{4}}}\\= q^{ \frac{-5}{4} - (\frac{-3}{4}) }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
11. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{4}{3}}}\\= y^{ \frac{1}{2} - \frac{4}{3} }= y^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ y^{5} }}=\frac{1}{\sqrt[6]{ y^{5} }}. \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y|}\\---------------\)
12. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{3}{2}}}\\= a^{ \frac{-1}{2} - \frac{3}{2} }= a^{-2}\\=\frac{1}{a^{2}}\\---------------\)