Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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