Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-2}{5}}}{q^{\frac{5}{2}}}\\= q^{ \frac{-2}{5} - \frac{5}{2} }= q^{\frac{-29}{10}}\\=\frac{1}{\sqrt[10]{ q^{29} }}\\=\frac{1}{|q^{2}|.\sqrt[10]{ q^{9} }}=\frac{1}{|q^{2}|.\sqrt[10]{ q^{9} }} \color{purple}{\frac{\sqrt[10]{ q }}{\sqrt[10]{ q }}} \\=\frac{\sqrt[10]{ q }}{|q^{3}|}\\---------------\)
2. \(\dfrac{a^{\frac{1}{6}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{1}{6} - (\frac{-1}{2}) }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
3. \(\dfrac{y^{\frac{-5}{3}}}{y^{\frac{3}{2}}}\\= y^{ \frac{-5}{3} - \frac{3}{2} }= y^{\frac{-19}{6}}\\=\frac{1}{\sqrt[6]{ y^{19} }}\\=\frac{1}{|y^{3}|.\sqrt[6]{ y }}=\frac{1}{|y^{3}|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{4}|}\\---------------\)
4. \(\dfrac{x^{\frac{-1}{5}}}{x^{\frac{4}{3}}}\\= x^{ \frac{-1}{5} - \frac{4}{3} }= x^{\frac{-23}{15}}\\=\frac{1}{\sqrt[15]{ x^{23} }}\\=\frac{1}{x.\sqrt[15]{ x^{8} }}=\frac{1}{x.\sqrt[15]{ x^{8} }} \color{purple}{\frac{\sqrt[15]{ x^{7} }}{\sqrt[15]{ x^{7} }}} \\=\frac{\sqrt[15]{ x^{7} }}{x^{2}}\\---------------\)
5. \(\dfrac{a^{-1}}{a^{\frac{5}{2}}}\\= a^{ -1 - \frac{5}{2} }= a^{\frac{-7}{2}}\\=\frac{1}{ \sqrt{ a^{7} } }\\=\frac{1}{|a^{3}|. \sqrt{ a } }=\frac{1}{|a^{3}|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{4}|}\\---------------\)
6. \(\dfrac{a^{\frac{-5}{3}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{-5}{3} - (\frac{-1}{2}) }= a^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ a^{7} }}\\=\frac{1}{|a|.\sqrt[6]{ a }}=\frac{1}{|a|.\sqrt[6]{ a }} \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a^{2}|}\\---------------\)
7. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{1}{5}}}\\= q^{ \frac{2}{3} - \frac{1}{5} }= q^{\frac{7}{15}}\\=\sqrt[15]{ q^{7} }\\---------------\)
8. \(\dfrac{x^{\frac{4}{5}}}{x^{\frac{1}{5}}}\\= x^{ \frac{4}{5} - \frac{1}{5} }= x^{\frac{3}{5}}\\=\sqrt[5]{ x^{3} }\\---------------\)
9. \(\dfrac{x^{\frac{4}{5}}}{x^{\frac{5}{2}}}\\= x^{ \frac{4}{5} - \frac{5}{2} }= x^{\frac{-17}{10}}\\=\frac{1}{\sqrt[10]{ x^{17} }}\\=\frac{1}{|x|.\sqrt[10]{ x^{7} }}=\frac{1}{|x|.\sqrt[10]{ x^{7} }} \color{purple}{\frac{\sqrt[10]{ x^{3} }}{\sqrt[10]{ x^{3} }}} \\=\frac{\sqrt[10]{ x^{3} }}{|x^{2}|}\\---------------\)
10. \(\dfrac{x^{\frac{5}{2}}}{x^{\frac{5}{4}}}\\= x^{ \frac{5}{2} - \frac{5}{4} }= x^{\frac{5}{4}}\\=\sqrt[4]{ x^{5} }=|x|.\sqrt[4]{ x }\\---------------\)
11. \(\dfrac{q^{\frac{-1}{5}}}{q^{\frac{-3}{2}}}\\= q^{ \frac{-1}{5} - (\frac{-3}{2}) }= q^{\frac{13}{10}}\\=\sqrt[10]{ q^{13} }=|q|.\sqrt[10]{ q^{3} }\\---------------\)
12. \(\dfrac{a^{-2}}{a^{\frac{4}{3}}}\\= a^{ -2 - \frac{4}{3} }= a^{\frac{-10}{3}}\\=\frac{1}{\sqrt[3]{ a^{10} }}\\=\frac{1}{a^{3}.\sqrt[3]{ a }}=\frac{1}{a^{3}.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{4}}\\---------------\)