Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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