Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{-4}{5}}}\\= a^{ \frac{-1}{2} - (\frac{-4}{5}) }= a^{\frac{3}{10}}\\=\sqrt[10]{ a^{3} }\\---------------\)
2. \(\dfrac{y^{\frac{-4}{5}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{-4}{5} - (\frac{-1}{3}) }= y^{\frac{-7}{15}}\\=\frac{1}{\sqrt[15]{ y^{7} }}=\frac{1}{\sqrt[15]{ y^{7} }}. \color{purple}{\frac{\sqrt[15]{ y^{8} }}{\sqrt[15]{ y^{8} }}} \\=\frac{\sqrt[15]{ y^{8} }}{y}\\---------------\)
3. \(\dfrac{a^{\frac{4}{3}}}{a^{\frac{3}{2}}}\\= a^{ \frac{4}{3} - \frac{3}{2} }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
4. \(\dfrac{y^{\frac{-5}{4}}}{y^{\frac{1}{3}}}\\= y^{ \frac{-5}{4} - \frac{1}{3} }= y^{\frac{-19}{12}}\\=\frac{1}{\sqrt[12]{ y^{19} }}\\=\frac{1}{|y|.\sqrt[12]{ y^{7} }}=\frac{1}{|y|.\sqrt[12]{ y^{7} }} \color{purple}{\frac{\sqrt[12]{ y^{5} }}{\sqrt[12]{ y^{5} }}} \\=\frac{\sqrt[12]{ y^{5} }}{|y^{2}|}\\---------------\)
5. \(\dfrac{a^{\frac{-4}{5}}}{a^{\frac{-5}{3}}}\\= a^{ \frac{-4}{5} - (\frac{-5}{3}) }= a^{\frac{13}{15}}\\=\sqrt[15]{ a^{13} }\\---------------\)
6. \(\dfrac{q^{-1}}{q^{1}}\\= q^{ -1 - 1 }= q^{-2}\\=\frac{1}{q^{2}}\\---------------\)
7. \(\dfrac{y^{\frac{1}{3}}}{y^{-1}}\\= y^{ \frac{1}{3} - (-1) }= y^{\frac{4}{3}}\\=\sqrt[3]{ y^{4} }=y.\sqrt[3]{ y }\\---------------\)
8. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{2}{3} - (\frac{-1}{2}) }= a^{\frac{7}{6}}\\=\sqrt[6]{ a^{7} }=|a|.\sqrt[6]{ a }\\---------------\)
9. \(\dfrac{q^{\frac{-5}{6}}}{q^{\frac{1}{2}}}\\= q^{ \frac{-5}{6} - \frac{1}{2} }= q^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ q^{4} }}\\=\frac{1}{q.\sqrt[3]{ q }}=\frac{1}{q.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{2}}\\---------------\)
10. \(\dfrac{a^{\frac{-5}{3}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{-5}{3} - (\frac{-1}{2}) }= a^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ a^{7} }}\\=\frac{1}{|a|.\sqrt[6]{ a }}=\frac{1}{|a|.\sqrt[6]{ a }} \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a^{2}|}\\---------------\)
11. \(\dfrac{a^{-1}}{a^{\frac{-3}{2}}}\\= a^{ -1 - (\frac{-3}{2}) }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
12. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{1}{2} - (\frac{-2}{3}) }= a^{\frac{7}{6}}\\=\sqrt[6]{ a^{7} }=|a|.\sqrt[6]{ a }\\---------------\)