Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-5}{2}}}{q^{\frac{-5}{3}}}\\= q^{ \frac{-5}{2} - (\frac{-5}{3}) }= q^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ q^{5} }}=\frac{1}{\sqrt[6]{ q^{5} }}. \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q|}\\---------------\)
2. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{-1}{6}}}\\= a^{ \frac{1}{3} - (\frac{-1}{6}) }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
3. \(\dfrac{a^{\frac{-4}{5}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{-4}{5} - (\frac{-1}{3}) }= a^{\frac{-7}{15}}\\=\frac{1}{\sqrt[15]{ a^{7} }}=\frac{1}{\sqrt[15]{ a^{7} }}. \color{purple}{\frac{\sqrt[15]{ a^{8} }}{\sqrt[15]{ a^{8} }}} \\=\frac{\sqrt[15]{ a^{8} }}{a}\\---------------\)
4. \(\dfrac{x^{\frac{-1}{3}}}{x^{-2}}\\= x^{ \frac{-1}{3} - (-2) }= x^{\frac{5}{3}}\\=\sqrt[3]{ x^{5} }=x.\sqrt[3]{ x^{2} }\\---------------\)
5. \(\dfrac{a^{\frac{-3}{2}}}{a^{1}}\\= a^{ \frac{-3}{2} - 1 }= a^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ a^{5} } }\\=\frac{1}{|a^{2}|. \sqrt{ a } }=\frac{1}{|a^{2}|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{3}|}\\---------------\)
6. \(\dfrac{x^{1}}{x^{\frac{-1}{4}}}\\= x^{ 1 - (\frac{-1}{4}) }= x^{\frac{5}{4}}\\=\sqrt[4]{ x^{5} }=|x|.\sqrt[4]{ x }\\---------------\)
7. \(\dfrac{q^{\frac{-2}{5}}}{q^{\frac{2}{3}}}\\= q^{ \frac{-2}{5} - \frac{2}{3} }= q^{\frac{-16}{15}}\\=\frac{1}{\sqrt[15]{ q^{16} }}\\=\frac{1}{q.\sqrt[15]{ q }}=\frac{1}{q.\sqrt[15]{ q }} \color{purple}{\frac{\sqrt[15]{ q^{14} }}{\sqrt[15]{ q^{14} }}} \\=\frac{\sqrt[15]{ q^{14} }}{q^{2}}\\---------------\)
8. \(\dfrac{x^{\frac{4}{3}}}{x^{\frac{-2}{3}}}\\= x^{ \frac{4}{3} - (\frac{-2}{3}) }= x^{2}\\\\---------------\)
9. \(\dfrac{a^{\frac{2}{3}}}{a^{2}}\\= a^{ \frac{2}{3} - 2 }= a^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ a^{4} }}\\=\frac{1}{a.\sqrt[3]{ a }}=\frac{1}{a.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{2}}\\---------------\)
10. \(\dfrac{q^{\frac{-1}{6}}}{q^{\frac{3}{5}}}\\= q^{ \frac{-1}{6} - \frac{3}{5} }= q^{\frac{-23}{30}}\\=\frac{1}{\sqrt[30]{ q^{23} }}=\frac{1}{\sqrt[30]{ q^{23} }}. \color{purple}{\frac{\sqrt[30]{ q^{7} }}{\sqrt[30]{ q^{7} }}} \\=\frac{\sqrt[30]{ q^{7} }}{|q|}\\---------------\)
11. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{-4}{5}}}\\= a^{ \frac{-1}{3} - (\frac{-4}{5}) }= a^{\frac{7}{15}}\\=\sqrt[15]{ a^{7} }\\---------------\)
12. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{3}{4}}}\\= q^{ \frac{1}{3} - \frac{3}{4} }= q^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ q^{5} }}=\frac{1}{\sqrt[12]{ q^{5} }}. \color{purple}{\frac{\sqrt[12]{ q^{7} }}{\sqrt[12]{ q^{7} }}} \\=\frac{\sqrt[12]{ q^{7} }}{|q|}\\---------------\)