Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{1}}{q^{\frac{-1}{2}}}\\= q^{ 1 - (\frac{-1}{2}) }= q^{\frac{3}{2}}\\= \sqrt{ q^{3} } =|q|. \sqrt{ q } \\---------------\)
2. \(\dfrac{y^{\frac{3}{4}}}{y^{\frac{-4}{5}}}\\= y^{ \frac{3}{4} - (\frac{-4}{5}) }= y^{\frac{31}{20}}\\=\sqrt[20]{ y^{31} }=|y|.\sqrt[20]{ y^{11} }\\---------------\)
3. \(\dfrac{a^{-1}}{a^{1}}\\= a^{ -1 - 1 }= a^{-2}\\=\frac{1}{a^{2}}\\---------------\)
4. \(\dfrac{y^{\frac{1}{5}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{1}{5} - (\frac{-1}{2}) }= y^{\frac{7}{10}}\\=\sqrt[10]{ y^{7} }\\---------------\)
5. \(\dfrac{q^{-1}}{q^{\frac{-1}{5}}}\\= q^{ -1 - (\frac{-1}{5}) }= q^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ q^{4} }}=\frac{1}{\sqrt[5]{ q^{4} }}. \color{purple}{\frac{\sqrt[5]{ q }}{\sqrt[5]{ q }}} \\=\frac{\sqrt[5]{ q }}{q}\\---------------\)
6. \(\dfrac{a^{\frac{-3}{5}}}{a^{\frac{-5}{2}}}\\= a^{ \frac{-3}{5} - (\frac{-5}{2}) }= a^{\frac{19}{10}}\\=\sqrt[10]{ a^{19} }=|a|.\sqrt[10]{ a^{9} }\\---------------\)
7. \(\dfrac{y^{\frac{3}{5}}}{y^{-1}}\\= y^{ \frac{3}{5} - (-1) }= y^{\frac{8}{5}}\\=\sqrt[5]{ y^{8} }=y.\sqrt[5]{ y^{3} }\\---------------\)
8. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{5}{3}}}\\= y^{ \frac{1}{2} - \frac{5}{3} }= y^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[6]{ y }}=\frac{1}{|y|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{2}|}\\---------------\)
9. \(\dfrac{a^{1}}{a^{\frac{3}{4}}}\\= a^{ 1 - \frac{3}{4} }= a^{\frac{1}{4}}\\=\sqrt[4]{ a }\\---------------\)
10. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{1}{2}}}\\= a^{ \frac{-1}{3} - \frac{1}{2} }= a^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ a^{5} }}=\frac{1}{\sqrt[6]{ a^{5} }}. \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a|}\\---------------\)
11. \(\dfrac{x^{\frac{-3}{4}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{-3}{4} - (\frac{-1}{3}) }= x^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ x^{5} }}=\frac{1}{\sqrt[12]{ x^{5} }}. \color{purple}{\frac{\sqrt[12]{ x^{7} }}{\sqrt[12]{ x^{7} }}} \\=\frac{\sqrt[12]{ x^{7} }}{|x|}\\---------------\)
12. \(\dfrac{x^{\frac{-3}{4}}}{x^{\frac{1}{6}}}\\= x^{ \frac{-3}{4} - \frac{1}{6} }= x^{\frac{-11}{12}}\\=\frac{1}{\sqrt[12]{ x^{11} }}=\frac{1}{\sqrt[12]{ x^{11} }}. \color{purple}{\frac{\sqrt[12]{ x }}{\sqrt[12]{ x }}} \\=\frac{\sqrt[12]{ x }}{|x|}\\---------------\)