Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-3}{2}}}{q^{\frac{-1}{6}}}\\= q^{ \frac{-3}{2} - (\frac{-1}{6}) }= q^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ q^{4} }}\\=\frac{1}{q.\sqrt[3]{ q }}=\frac{1}{q.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{2}}\\---------------\)
2. \(\dfrac{a^{\frac{1}{4}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{1}{4} - (\frac{-2}{3}) }= a^{\frac{11}{12}}\\=\sqrt[12]{ a^{11} }\\---------------\)
3. \(\dfrac{y^{\frac{-2}{5}}}{y^{\frac{-3}{5}}}\\= y^{ \frac{-2}{5} - (\frac{-3}{5}) }= y^{\frac{1}{5}}\\=\sqrt[5]{ y }\\---------------\)
4. \(\dfrac{q^{\frac{-2}{5}}}{q^{\frac{-5}{3}}}\\= q^{ \frac{-2}{5} - (\frac{-5}{3}) }= q^{\frac{19}{15}}\\=\sqrt[15]{ q^{19} }=q.\sqrt[15]{ q^{4} }\\---------------\)
5. \(\dfrac{x^{\frac{4}{3}}}{x^{\frac{-3}{5}}}\\= x^{ \frac{4}{3} - (\frac{-3}{5}) }= x^{\frac{29}{15}}\\=\sqrt[15]{ x^{29} }=x.\sqrt[15]{ x^{14} }\\---------------\)
6. \(\dfrac{a^{\frac{-5}{2}}}{a^{1}}\\= a^{ \frac{-5}{2} - 1 }= a^{\frac{-7}{2}}\\=\frac{1}{ \sqrt{ a^{7} } }\\=\frac{1}{|a^{3}|. \sqrt{ a } }=\frac{1}{|a^{3}|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{4}|}\\---------------\)
7. \(\dfrac{a^{\frac{5}{3}}}{a^{\frac{-3}{5}}}\\= a^{ \frac{5}{3} - (\frac{-3}{5}) }= a^{\frac{34}{15}}\\=\sqrt[15]{ a^{34} }=a^{2}.\sqrt[15]{ a^{4} }\\---------------\)
8. \(\dfrac{q^{-1}}{q^{1}}\\= q^{ -1 - 1 }= q^{-2}\\=\frac{1}{q^{2}}\\---------------\)
9. \(\dfrac{x^{1}}{x^{\frac{5}{2}}}\\= x^{ 1 - \frac{5}{2} }= x^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ x^{3} } }\\=\frac{1}{|x|. \sqrt{ x } }=\frac{1}{|x|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{2}|}\\---------------\)
10. \(\dfrac{x^{\frac{4}{3}}}{x^{\frac{5}{6}}}\\= x^{ \frac{4}{3} - \frac{5}{6} }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
11. \(\dfrac{q^{\frac{1}{4}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{1}{4} - (\frac{-1}{2}) }= q^{\frac{3}{4}}\\=\sqrt[4]{ q^{3} }\\---------------\)
12. \(\dfrac{x^{-1}}{x^{\frac{-5}{2}}}\\= x^{ -1 - (\frac{-5}{2}) }= x^{\frac{3}{2}}\\= \sqrt{ x^{3} } =|x|. \sqrt{ x } \\---------------\)