Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{5}{3}}}{a^{2}}\\= a^{ \frac{5}{3} - 2 }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
2. \(\dfrac{y^{\frac{-4}{5}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{-4}{5} - (\frac{-2}{3}) }= y^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ y^{2} }}=\frac{1}{\sqrt[15]{ y^{2} }}. \color{purple}{\frac{\sqrt[15]{ y^{13} }}{\sqrt[15]{ y^{13} }}} \\=\frac{\sqrt[15]{ y^{13} }}{y}\\---------------\)
3. \(\dfrac{x^{1}}{x^{-1}}\\= x^{ 1 - (-1) }= x^{2}\\\\---------------\)
4. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{-3}{4}}}\\= y^{ \frac{-2}{3} - (\frac{-3}{4}) }= y^{\frac{1}{12}}\\=\sqrt[12]{ y }\\---------------\)
5. \(\dfrac{a^{\frac{-1}{4}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{-1}{4} - (\frac{-1}{2}) }= a^{\frac{1}{4}}\\=\sqrt[4]{ a }\\---------------\)
6. \(\dfrac{q^{\frac{-5}{2}}}{q^{\frac{-5}{2}}}\\= q^{ \frac{-5}{2} - (\frac{-5}{2}) }= q^{0}\\=1\\---------------\)
7. \(\dfrac{q^{\frac{-5}{6}}}{q^{\frac{-1}{5}}}\\= q^{ \frac{-5}{6} - (\frac{-1}{5}) }= q^{\frac{-19}{30}}\\=\frac{1}{\sqrt[30]{ q^{19} }}=\frac{1}{\sqrt[30]{ q^{19} }}. \color{purple}{\frac{\sqrt[30]{ q^{11} }}{\sqrt[30]{ q^{11} }}} \\=\frac{\sqrt[30]{ q^{11} }}{|q|}\\---------------\)
8. \(\dfrac{q^{-1}}{q^{\frac{-5}{4}}}\\= q^{ -1 - (\frac{-5}{4}) }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
9. \(\dfrac{a^{1}}{a^{\frac{-5}{6}}}\\= a^{ 1 - (\frac{-5}{6}) }= a^{\frac{11}{6}}\\=\sqrt[6]{ a^{11} }=|a|.\sqrt[6]{ a^{5} }\\---------------\)
10. \(\dfrac{q^{1}}{q^{1}}\\= q^{ 1 - 1 }= q^{0}\\=1\\---------------\)
11. \(\dfrac{y^{-1}}{y^{\frac{3}{5}}}\\= y^{ -1 - \frac{3}{5} }= y^{\frac{-8}{5}}\\=\frac{1}{\sqrt[5]{ y^{8} }}\\=\frac{1}{y.\sqrt[5]{ y^{3} }}=\frac{1}{y.\sqrt[5]{ y^{3} }} \color{purple}{\frac{\sqrt[5]{ y^{2} }}{\sqrt[5]{ y^{2} }}} \\=\frac{\sqrt[5]{ y^{2} }}{y^{2}}\\---------------\)
12. \(\dfrac{a^{\frac{1}{6}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{1}{6} - (\frac{-1}{2}) }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)