Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-3}{4}}}{a^{\frac{-4}{5}}}\\= a^{ \frac{-3}{4} - (\frac{-4}{5}) }= a^{\frac{1}{20}}\\=\sqrt[20]{ a }\\---------------\)
2. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{1}{2}}}\\= x^{ \frac{1}{2} - \frac{1}{2} }= x^{0}\\=1\\---------------\)
3. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{2}{3}}}\\= a^{ \frac{2}{3} - \frac{2}{3} }= a^{0}\\=1\\---------------\)
4. \(\dfrac{x^{\frac{-1}{2}}}{x^{1}}\\= x^{ \frac{-1}{2} - 1 }= x^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ x^{3} } }\\=\frac{1}{|x|. \sqrt{ x } }=\frac{1}{|x|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{2}|}\\---------------\)
5. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{-4}{3}}}\\= y^{ \frac{2}{3} - (\frac{-4}{3}) }= y^{2}\\\\---------------\)
6. \(\dfrac{q^{\frac{-5}{6}}}{q^{\frac{-1}{4}}}\\= q^{ \frac{-5}{6} - (\frac{-1}{4}) }= q^{\frac{-7}{12}}\\=\frac{1}{\sqrt[12]{ q^{7} }}=\frac{1}{\sqrt[12]{ q^{7} }}. \color{purple}{\frac{\sqrt[12]{ q^{5} }}{\sqrt[12]{ q^{5} }}} \\=\frac{\sqrt[12]{ q^{5} }}{|q|}\\---------------\)
7. \(\dfrac{a^{\frac{1}{5}}}{a^{\frac{-3}{4}}}\\= a^{ \frac{1}{5} - (\frac{-3}{4}) }= a^{\frac{19}{20}}\\=\sqrt[20]{ a^{19} }\\---------------\)
8. \(\dfrac{q^{-1}}{q^{\frac{4}{3}}}\\= q^{ -1 - \frac{4}{3} }= q^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ q^{7} }}\\=\frac{1}{q^{2}.\sqrt[3]{ q }}=\frac{1}{q^{2}.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{3}}\\---------------\)
9. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{-1}{2} - (\frac{-1}{2}) }= y^{0}\\=1\\---------------\)
10. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{3}{5}}}\\= q^{ \frac{1}{3} - \frac{3}{5} }= q^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ q^{4} }}=\frac{1}{\sqrt[15]{ q^{4} }}. \color{purple}{\frac{\sqrt[15]{ q^{11} }}{\sqrt[15]{ q^{11} }}} \\=\frac{\sqrt[15]{ q^{11} }}{q}\\---------------\)
11. \(\dfrac{y^{-1}}{y^{\frac{-2}{3}}}\\= y^{ -1 - (\frac{-2}{3}) }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
12. \(\dfrac{x^{\frac{2}{5}}}{x^{\frac{3}{5}}}\\= x^{ \frac{2}{5} - \frac{3}{5} }= x^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ x }}=\frac{1}{\sqrt[5]{ x }}. \color{purple}{\frac{\sqrt[5]{ x^{4} }}{\sqrt[5]{ x^{4} }}} \\=\frac{\sqrt[5]{ x^{4} }}{x}\\---------------\)