Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-1}{2}}}{a^{1}}\\= a^{ \frac{-1}{2} - 1 }= a^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ a^{3} } }\\=\frac{1}{|a|. \sqrt{ a } }=\frac{1}{|a|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{2}|}\\---------------\)
2. \(\dfrac{a^{\frac{-3}{4}}}{a^{\frac{-3}{5}}}\\= a^{ \frac{-3}{4} - (\frac{-3}{5}) }= a^{\frac{-3}{20}}\\=\frac{1}{\sqrt[20]{ a^{3} }}=\frac{1}{\sqrt[20]{ a^{3} }}. \color{purple}{\frac{\sqrt[20]{ a^{17} }}{\sqrt[20]{ a^{17} }}} \\=\frac{\sqrt[20]{ a^{17} }}{|a|}\\---------------\)
3. \(\dfrac{q^{\frac{5}{6}}}{q^{\frac{-5}{2}}}\\= q^{ \frac{5}{6} - (\frac{-5}{2}) }= q^{\frac{10}{3}}\\=\sqrt[3]{ q^{10} }=q^{3}.\sqrt[3]{ q }\\---------------\)
4. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{5}{4}}}\\= x^{ \frac{-1}{2} - \frac{5}{4} }= x^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ x^{7} }}\\=\frac{1}{|x|.\sqrt[4]{ x^{3} }}=\frac{1}{|x|.\sqrt[4]{ x^{3} }} \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x^{2}|}\\---------------\)
5. \(\dfrac{q^{\frac{-4}{5}}}{q^{1}}\\= q^{ \frac{-4}{5} - 1 }= q^{\frac{-9}{5}}\\=\frac{1}{\sqrt[5]{ q^{9} }}\\=\frac{1}{q.\sqrt[5]{ q^{4} }}=\frac{1}{q.\sqrt[5]{ q^{4} }} \color{purple}{\frac{\sqrt[5]{ q }}{\sqrt[5]{ q }}} \\=\frac{\sqrt[5]{ q }}{q^{2}}\\---------------\)
6. \(\dfrac{a^{\frac{-5}{4}}}{a^{\frac{2}{5}}}\\= a^{ \frac{-5}{4} - \frac{2}{5} }= a^{\frac{-33}{20}}\\=\frac{1}{\sqrt[20]{ a^{33} }}\\=\frac{1}{|a|.\sqrt[20]{ a^{13} }}=\frac{1}{|a|.\sqrt[20]{ a^{13} }} \color{purple}{\frac{\sqrt[20]{ a^{7} }}{\sqrt[20]{ a^{7} }}} \\=\frac{\sqrt[20]{ a^{7} }}{|a^{2}|}\\---------------\)
7. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{-1}{4}}}\\= q^{ \frac{-2}{3} - (\frac{-1}{4}) }= q^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ q^{5} }}=\frac{1}{\sqrt[12]{ q^{5} }}. \color{purple}{\frac{\sqrt[12]{ q^{7} }}{\sqrt[12]{ q^{7} }}} \\=\frac{\sqrt[12]{ q^{7} }}{|q|}\\---------------\)
8. \(\dfrac{y^{-2}}{y^{\frac{1}{3}}}\\= y^{ -2 - \frac{1}{3} }= y^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ y^{7} }}\\=\frac{1}{y^{2}.\sqrt[3]{ y }}=\frac{1}{y^{2}.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{3}}\\---------------\)
9. \(\dfrac{x^{\frac{-3}{4}}}{x^{\frac{4}{3}}}\\= x^{ \frac{-3}{4} - \frac{4}{3} }= x^{\frac{-25}{12}}\\=\frac{1}{\sqrt[12]{ x^{25} }}\\=\frac{1}{|x^{2}|.\sqrt[12]{ x }}=\frac{1}{|x^{2}|.\sqrt[12]{ x }} \color{purple}{\frac{\sqrt[12]{ x^{11} }}{\sqrt[12]{ x^{11} }}} \\=\frac{\sqrt[12]{ x^{11} }}{|x^{3}|}\\---------------\)
10. \(\dfrac{x^{\frac{3}{4}}}{x^{\frac{4}{3}}}\\= x^{ \frac{3}{4} - \frac{4}{3} }= x^{\frac{-7}{12}}\\=\frac{1}{\sqrt[12]{ x^{7} }}=\frac{1}{\sqrt[12]{ x^{7} }}. \color{purple}{\frac{\sqrt[12]{ x^{5} }}{\sqrt[12]{ x^{5} }}} \\=\frac{\sqrt[12]{ x^{5} }}{|x|}\\---------------\)
11. \(\dfrac{q^{-1}}{q^{\frac{-3}{4}}}\\= q^{ -1 - (\frac{-3}{4}) }= q^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ q }}=\frac{1}{\sqrt[4]{ q }}. \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q|}\\---------------\)
12. \(\dfrac{a^{\frac{4}{3}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{4}{3} - (\frac{-1}{3}) }= a^{\frac{5}{3}}\\=\sqrt[3]{ a^{5} }=a.\sqrt[3]{ a^{2} }\\---------------\)