Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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