Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-3}{4}}}{q^{\frac{4}{3}}}\\= q^{ \frac{-3}{4} - \frac{4}{3} }= q^{\frac{-25}{12}}\\=\frac{1}{\sqrt[12]{ q^{25} }}\\=\frac{1}{|q^{2}|.\sqrt[12]{ q }}=\frac{1}{|q^{2}|.\sqrt[12]{ q }} \color{purple}{\frac{\sqrt[12]{ q^{11} }}{\sqrt[12]{ q^{11} }}} \\=\frac{\sqrt[12]{ q^{11} }}{|q^{3}|}\\---------------\)
2. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{-5}{4}}}\\= a^{ \frac{-1}{3} - (\frac{-5}{4}) }= a^{\frac{11}{12}}\\=\sqrt[12]{ a^{11} }\\---------------\)
3. \(\dfrac{x^{\frac{-1}{4}}}{x^{\frac{3}{2}}}\\= x^{ \frac{-1}{4} - \frac{3}{2} }= x^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ x^{7} }}\\=\frac{1}{|x|.\sqrt[4]{ x^{3} }}=\frac{1}{|x|.\sqrt[4]{ x^{3} }} \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x^{2}|}\\---------------\)
4. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{-2}{3} - (\frac{-1}{2}) }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
5. \(\dfrac{q^{\frac{3}{5}}}{q^{-1}}\\= q^{ \frac{3}{5} - (-1) }= q^{\frac{8}{5}}\\=\sqrt[5]{ q^{8} }=q.\sqrt[5]{ q^{3} }\\---------------\)
6. \(\dfrac{x^{\frac{-5}{3}}}{x^{-1}}\\= x^{ \frac{-5}{3} - (-1) }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
7. \(\dfrac{x^{-1}}{x^{\frac{-4}{5}}}\\= x^{ -1 - (\frac{-4}{5}) }= x^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ x }}=\frac{1}{\sqrt[5]{ x }}. \color{purple}{\frac{\sqrt[5]{ x^{4} }}{\sqrt[5]{ x^{4} }}} \\=\frac{\sqrt[5]{ x^{4} }}{x}\\---------------\)
8. \(\dfrac{x^{\frac{-5}{6}}}{x^{-1}}\\= x^{ \frac{-5}{6} - (-1) }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
9. \(\dfrac{x^{\frac{-1}{5}}}{x^{1}}\\= x^{ \frac{-1}{5} - 1 }= x^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ x^{6} }}\\=\frac{1}{x.\sqrt[5]{ x }}=\frac{1}{x.\sqrt[5]{ x }} \color{purple}{\frac{\sqrt[5]{ x^{4} }}{\sqrt[5]{ x^{4} }}} \\=\frac{\sqrt[5]{ x^{4} }}{x^{2}}\\---------------\)
10. \(\dfrac{x^{\frac{-5}{3}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{-5}{3} - (\frac{-1}{3}) }= x^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ x^{4} }}\\=\frac{1}{x.\sqrt[3]{ x }}=\frac{1}{x.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{2}}\\---------------\)
11. \(\dfrac{q^{\frac{1}{6}}}{q^{\frac{3}{5}}}\\= q^{ \frac{1}{6} - \frac{3}{5} }= q^{\frac{-13}{30}}\\=\frac{1}{\sqrt[30]{ q^{13} }}=\frac{1}{\sqrt[30]{ q^{13} }}. \color{purple}{\frac{\sqrt[30]{ q^{17} }}{\sqrt[30]{ q^{17} }}} \\=\frac{\sqrt[30]{ q^{17} }}{|q|}\\---------------\)
12. \(\dfrac{q^{\frac{-4}{5}}}{q^{1}}\\= q^{ \frac{-4}{5} - 1 }= q^{\frac{-9}{5}}\\=\frac{1}{\sqrt[5]{ q^{9} }}\\=\frac{1}{q.\sqrt[5]{ q^{4} }}=\frac{1}{q.\sqrt[5]{ q^{4} }} \color{purple}{\frac{\sqrt[5]{ q }}{\sqrt[5]{ q }}} \\=\frac{\sqrt[5]{ q }}{q^{2}}\\---------------\)