Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{5}{3}}}{q^{\frac{2}{3}}}\\= q^{ \frac{5}{3} - \frac{2}{3} }= q^{1}\\\\---------------\)
2. \(\dfrac{q^{\frac{-1}{4}}}{q^{\frac{4}{5}}}\\= q^{ \frac{-1}{4} - \frac{4}{5} }= q^{\frac{-21}{20}}\\=\frac{1}{\sqrt[20]{ q^{21} }}\\=\frac{1}{|q|.\sqrt[20]{ q }}=\frac{1}{|q|.\sqrt[20]{ q }} \color{purple}{\frac{\sqrt[20]{ q^{19} }}{\sqrt[20]{ q^{19} }}} \\=\frac{\sqrt[20]{ q^{19} }}{|q^{2}|}\\---------------\)
3. \(\dfrac{a^{1}}{a^{\frac{-5}{2}}}\\= a^{ 1 - (\frac{-5}{2}) }= a^{\frac{7}{2}}\\= \sqrt{ a^{7} } =|a^{3}|. \sqrt{ a } \\---------------\)
4. \(\dfrac{x^{\frac{-5}{2}}}{x^{\frac{5}{2}}}\\= x^{ \frac{-5}{2} - \frac{5}{2} }= x^{-5}\\=\frac{1}{x^{5}}\\---------------\)
5. \(\dfrac{x^{\frac{2}{5}}}{x^{1}}\\= x^{ \frac{2}{5} - 1 }= x^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ x^{3} }}=\frac{1}{\sqrt[5]{ x^{3} }}. \color{purple}{\frac{\sqrt[5]{ x^{2} }}{\sqrt[5]{ x^{2} }}} \\=\frac{\sqrt[5]{ x^{2} }}{x}\\---------------\)
6. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{1}{6}}}\\= x^{ \frac{1}{2} - \frac{1}{6} }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
7. \(\dfrac{y^{\frac{-4}{5}}}{y^{\frac{-3}{4}}}\\= y^{ \frac{-4}{5} - (\frac{-3}{4}) }= y^{\frac{-1}{20}}\\=\frac{1}{\sqrt[20]{ y }}=\frac{1}{\sqrt[20]{ y }}. \color{purple}{\frac{\sqrt[20]{ y^{19} }}{\sqrt[20]{ y^{19} }}} \\=\frac{\sqrt[20]{ y^{19} }}{|y|}\\---------------\)
8. \(\dfrac{x^{\frac{-5}{3}}}{x^{\frac{-3}{5}}}\\= x^{ \frac{-5}{3} - (\frac{-3}{5}) }= x^{\frac{-16}{15}}\\=\frac{1}{\sqrt[15]{ x^{16} }}\\=\frac{1}{x.\sqrt[15]{ x }}=\frac{1}{x.\sqrt[15]{ x }} \color{purple}{\frac{\sqrt[15]{ x^{14} }}{\sqrt[15]{ x^{14} }}} \\=\frac{\sqrt[15]{ x^{14} }}{x^{2}}\\---------------\)
9. \(\dfrac{a^{\frac{1}{4}}}{a^{\frac{1}{2}}}\\= a^{ \frac{1}{4} - \frac{1}{2} }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
10. \(\dfrac{y^{\frac{-3}{2}}}{y^{\frac{-4}{3}}}\\= y^{ \frac{-3}{2} - (\frac{-4}{3}) }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
11. \(\dfrac{q^{1}}{q^{\frac{-1}{2}}}\\= q^{ 1 - (\frac{-1}{2}) }= q^{\frac{3}{2}}\\= \sqrt{ q^{3} } =|q|. \sqrt{ q } \\---------------\)
12. \(\dfrac{q^{\frac{1}{5}}}{q^{\frac{1}{5}}}\\= q^{ \frac{1}{5} - \frac{1}{5} }= q^{0}\\=1\\---------------\)