Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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