Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-5}{3}}}{q^{\frac{-5}{4}}}\\= q^{ \frac{-5}{3} - (\frac{-5}{4}) }= q^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ q^{5} }}=\frac{1}{\sqrt[12]{ q^{5} }}. \color{purple}{\frac{\sqrt[12]{ q^{7} }}{\sqrt[12]{ q^{7} }}} \\=\frac{\sqrt[12]{ q^{7} }}{|q|}\\---------------\)
2. \(\dfrac{q^{\frac{1}{3}}}{q^{2}}\\= q^{ \frac{1}{3} - 2 }= q^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ q^{5} }}\\=\frac{1}{q.\sqrt[3]{ q^{2} }}=\frac{1}{q.\sqrt[3]{ q^{2} }} \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{2}}\\---------------\)
3. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{-5}{3}}}\\= x^{ \frac{2}{3} - (\frac{-5}{3}) }= x^{\frac{7}{3}}\\=\sqrt[3]{ x^{7} }=x^{2}.\sqrt[3]{ x }\\---------------\)
4. \(\dfrac{q^{\frac{2}{5}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{2}{5} - (\frac{-2}{3}) }= q^{\frac{16}{15}}\\=\sqrt[15]{ q^{16} }=q.\sqrt[15]{ q }\\---------------\)
5. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{3}{4}}}\\= a^{ \frac{1}{3} - \frac{3}{4} }= a^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ a^{5} }}=\frac{1}{\sqrt[12]{ a^{5} }}. \color{purple}{\frac{\sqrt[12]{ a^{7} }}{\sqrt[12]{ a^{7} }}} \\=\frac{\sqrt[12]{ a^{7} }}{|a|}\\---------------\)
6. \(\dfrac{a^{-1}}{a^{\frac{-5}{6}}}\\= a^{ -1 - (\frac{-5}{6}) }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
7. \(\dfrac{q^{\frac{-3}{5}}}{q^{\frac{3}{2}}}\\= q^{ \frac{-3}{5} - \frac{3}{2} }= q^{\frac{-21}{10}}\\=\frac{1}{\sqrt[10]{ q^{21} }}\\=\frac{1}{|q^{2}|.\sqrt[10]{ q }}=\frac{1}{|q^{2}|.\sqrt[10]{ q }} \color{purple}{\frac{\sqrt[10]{ q^{9} }}{\sqrt[10]{ q^{9} }}} \\=\frac{\sqrt[10]{ q^{9} }}{|q^{3}|}\\---------------\)
8. \(\dfrac{x^{\frac{5}{4}}}{x^{\frac{5}{2}}}\\= x^{ \frac{5}{4} - \frac{5}{2} }= x^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ x^{5} }}\\=\frac{1}{|x|.\sqrt[4]{ x }}=\frac{1}{|x|.\sqrt[4]{ x }} \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x^{2}|}\\---------------\)
9. \(\dfrac{q^{\frac{-4}{3}}}{q^{\frac{-5}{6}}}\\= q^{ \frac{-4}{3} - (\frac{-5}{6}) }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
10. \(\dfrac{y^{\frac{-5}{2}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{-5}{2} - (\frac{-2}{3}) }= y^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ y^{11} }}\\=\frac{1}{|y|.\sqrt[6]{ y^{5} }}=\frac{1}{|y|.\sqrt[6]{ y^{5} }} \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y^{2}|}\\---------------\)
11. \(\dfrac{x^{\frac{2}{5}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{2}{5} - (\frac{-1}{2}) }= x^{\frac{9}{10}}\\=\sqrt[10]{ x^{9} }\\---------------\)
12. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{-4}{3}}}\\= q^{ \frac{-2}{3} - (\frac{-4}{3}) }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)