Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-5}{6}}}{q^{\frac{-1}{4}}}\\= q^{ \frac{-5}{6} - (\frac{-1}{4}) }= q^{\frac{-7}{12}}\\=\frac{1}{\sqrt[12]{ q^{7} }}=\frac{1}{\sqrt[12]{ q^{7} }}. \color{purple}{\frac{\sqrt[12]{ q^{5} }}{\sqrt[12]{ q^{5} }}} \\=\frac{\sqrt[12]{ q^{5} }}{|q|}\\---------------\)
2. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{-1}{2} - (\frac{-1}{2}) }= y^{0}\\=1\\---------------\)
3. \(\dfrac{x^{-1}}{x^{1}}\\= x^{ -1 - 1 }= x^{-2}\\=\frac{1}{x^{2}}\\---------------\)
4. \(\dfrac{a^{\frac{-1}{2}}}{a^{-1}}\\= a^{ \frac{-1}{2} - (-1) }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
5. \(\dfrac{q^{\frac{4}{3}}}{q^{\frac{-4}{5}}}\\= q^{ \frac{4}{3} - (\frac{-4}{5}) }= q^{\frac{32}{15}}\\=\sqrt[15]{ q^{32} }=q^{2}.\sqrt[15]{ q^{2} }\\---------------\)
6. \(\dfrac{a^{\frac{-5}{3}}}{a^{\frac{-4}{5}}}\\= a^{ \frac{-5}{3} - (\frac{-4}{5}) }= a^{\frac{-13}{15}}\\=\frac{1}{\sqrt[15]{ a^{13} }}=\frac{1}{\sqrt[15]{ a^{13} }}. \color{purple}{\frac{\sqrt[15]{ a^{2} }}{\sqrt[15]{ a^{2} }}} \\=\frac{\sqrt[15]{ a^{2} }}{a}\\---------------\)
7. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{-2}{3} - (\frac{-1}{2}) }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
8. \(\dfrac{x^{-1}}{x^{\frac{-5}{2}}}\\= x^{ -1 - (\frac{-5}{2}) }= x^{\frac{3}{2}}\\= \sqrt{ x^{3} } =|x|. \sqrt{ x } \\---------------\)
9. \(\dfrac{y^{\frac{3}{2}}}{y^{\frac{3}{4}}}\\= y^{ \frac{3}{2} - \frac{3}{4} }= y^{\frac{3}{4}}\\=\sqrt[4]{ y^{3} }\\---------------\)
10. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{2}{5}}}\\= q^{ \frac{1}{3} - \frac{2}{5} }= q^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ q }}=\frac{1}{\sqrt[15]{ q }}. \color{purple}{\frac{\sqrt[15]{ q^{14} }}{\sqrt[15]{ q^{14} }}} \\=\frac{\sqrt[15]{ q^{14} }}{q}\\---------------\)
11. \(\dfrac{x^{\frac{-4}{5}}}{x^{-1}}\\= x^{ \frac{-4}{5} - (-1) }= x^{\frac{1}{5}}\\=\sqrt[5]{ x }\\---------------\)
12. \(\dfrac{q^{-1}}{q^{\frac{-3}{2}}}\\= q^{ -1 - (\frac{-3}{2}) }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)