Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-4}{5}}}{q^{\frac{3}{2}}}\\= q^{ \frac{-4}{5} - \frac{3}{2} }= q^{\frac{-23}{10}}\\=\frac{1}{\sqrt[10]{ q^{23} }}\\=\frac{1}{|q^{2}|.\sqrt[10]{ q^{3} }}=\frac{1}{|q^{2}|.\sqrt[10]{ q^{3} }} \color{purple}{\frac{\sqrt[10]{ q^{7} }}{\sqrt[10]{ q^{7} }}} \\=\frac{\sqrt[10]{ q^{7} }}{|q^{3}|}\\---------------\)
2. \(\dfrac{x^{\frac{3}{4}}}{x^{\frac{-2}{3}}}\\= x^{ \frac{3}{4} - (\frac{-2}{3}) }= x^{\frac{17}{12}}\\=\sqrt[12]{ x^{17} }=|x|.\sqrt[12]{ x^{5} }\\---------------\)
3. \(\dfrac{q^{\frac{-1}{3}}}{q^{-1}}\\= q^{ \frac{-1}{3} - (-1) }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
4. \(\dfrac{a^{\frac{4}{3}}}{a^{\frac{3}{2}}}\\= a^{ \frac{4}{3} - \frac{3}{2} }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
5. \(\dfrac{a^{\frac{-1}{2}}}{a^{-1}}\\= a^{ \frac{-1}{2} - (-1) }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
6. \(\dfrac{a^{\frac{-1}{2}}}{a^{1}}\\= a^{ \frac{-1}{2} - 1 }= a^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ a^{3} } }\\=\frac{1}{|a|. \sqrt{ a } }=\frac{1}{|a|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{2}|}\\---------------\)
7. \(\dfrac{q^{\frac{4}{3}}}{q^{\frac{-5}{2}}}\\= q^{ \frac{4}{3} - (\frac{-5}{2}) }= q^{\frac{23}{6}}\\=\sqrt[6]{ q^{23} }=|q^{3}|.\sqrt[6]{ q^{5} }\\---------------\)
8. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{4}{3}}}\\= a^{ \frac{2}{3} - \frac{4}{3} }= a^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ a^{2} }}=\frac{1}{\sqrt[3]{ a^{2} }}. \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a}\\---------------\)
9. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{-2}{5}}}\\= y^{ \frac{-1}{3} - (\frac{-2}{5}) }= y^{\frac{1}{15}}\\=\sqrt[15]{ y }\\---------------\)
10. \(\dfrac{x^{\frac{-3}{5}}}{x^{\frac{1}{3}}}\\= x^{ \frac{-3}{5} - \frac{1}{3} }= x^{\frac{-14}{15}}\\=\frac{1}{\sqrt[15]{ x^{14} }}=\frac{1}{\sqrt[15]{ x^{14} }}. \color{purple}{\frac{\sqrt[15]{ x }}{\sqrt[15]{ x }}} \\=\frac{\sqrt[15]{ x }}{x}\\---------------\)
11. \(\dfrac{x^{\frac{-5}{4}}}{x^{-2}}\\= x^{ \frac{-5}{4} - (-2) }= x^{\frac{3}{4}}\\=\sqrt[4]{ x^{3} }\\---------------\)
12. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{5}{3}}}\\= a^{ \frac{-1}{2} - \frac{5}{3} }= a^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ a^{13} }}\\=\frac{1}{|a^{2}|.\sqrt[6]{ a }}=\frac{1}{|a^{2}|.\sqrt[6]{ a }} \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a^{3}|}\\---------------\)