Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-3}{2}}}{q^{\frac{-4}{3}}}\\= q^{ \frac{-3}{2} - (\frac{-4}{3}) }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)
2. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{5}{2}}}\\= x^{ \frac{2}{3} - \frac{5}{2} }= x^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ x^{11} }}\\=\frac{1}{|x|.\sqrt[6]{ x^{5} }}=\frac{1}{|x|.\sqrt[6]{ x^{5} }} \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x^{2}|}\\---------------\)
3. \(\dfrac{q^{\frac{-4}{3}}}{q^{\frac{5}{2}}}\\= q^{ \frac{-4}{3} - \frac{5}{2} }= q^{\frac{-23}{6}}\\=\frac{1}{\sqrt[6]{ q^{23} }}\\=\frac{1}{|q^{3}|.\sqrt[6]{ q^{5} }}=\frac{1}{|q^{3}|.\sqrt[6]{ q^{5} }} \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q^{4}|}\\---------------\)
4. \(\dfrac{x^{\frac{-3}{2}}}{x^{\frac{5}{6}}}\\= x^{ \frac{-3}{2} - \frac{5}{6} }= x^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ x^{7} }}\\=\frac{1}{x^{2}.\sqrt[3]{ x }}=\frac{1}{x^{2}.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{3}}\\---------------\)
5. \(\dfrac{a^{\frac{3}{4}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{3}{4} - (\frac{-2}{3}) }= a^{\frac{17}{12}}\\=\sqrt[12]{ a^{17} }=|a|.\sqrt[12]{ a^{5} }\\---------------\)
6. \(\dfrac{q^{1}}{q^{\frac{5}{2}}}\\= q^{ 1 - \frac{5}{2} }= q^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ q^{3} } }\\=\frac{1}{|q|. \sqrt{ q } }=\frac{1}{|q|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{2}|}\\---------------\)
7. \(\dfrac{q^{\frac{-5}{3}}}{q^{-2}}\\= q^{ \frac{-5}{3} - (-2) }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
8. \(\dfrac{a^{\frac{1}{6}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{1}{6} - (\frac{-1}{2}) }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
9. \(\dfrac{a^{\frac{-1}{6}}}{a^{\frac{5}{6}}}\\= a^{ \frac{-1}{6} - \frac{5}{6} }= a^{-1}\\=\frac{1}{a}\\---------------\)
10. \(\dfrac{x^{\frac{4}{3}}}{x^{\frac{-5}{4}}}\\= x^{ \frac{4}{3} - (\frac{-5}{4}) }= x^{\frac{31}{12}}\\=\sqrt[12]{ x^{31} }=|x^{2}|.\sqrt[12]{ x^{7} }\\---------------\)
11. \(\dfrac{y^{\frac{-1}{6}}}{y^{\frac{1}{3}}}\\= y^{ \frac{-1}{6} - \frac{1}{3} }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
12. \(\dfrac{x^{1}}{x^{\frac{-4}{3}}}\\= x^{ 1 - (\frac{-4}{3}) }= x^{\frac{7}{3}}\\=\sqrt[3]{ x^{7} }=x^{2}.\sqrt[3]{ x }\\---------------\)