Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{2}}{a^{\frac{-2}{3}}}\\= a^{ 2 - (\frac{-2}{3}) }= a^{\frac{8}{3}}\\=\sqrt[3]{ a^{8} }=a^{2}.\sqrt[3]{ a^{2} }\\---------------\)
2. \(\dfrac{q^{\frac{-4}{3}}}{q^{1}}\\= q^{ \frac{-4}{3} - 1 }= q^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ q^{7} }}\\=\frac{1}{q^{2}.\sqrt[3]{ q }}=\frac{1}{q^{2}.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{3}}\\---------------\)
3. \(\dfrac{x^{-1}}{x^{1}}\\= x^{ -1 - 1 }= x^{-2}\\=\frac{1}{x^{2}}\\---------------\)
4. \(\dfrac{x^{\frac{-4}{5}}}{x^{\frac{3}{4}}}\\= x^{ \frac{-4}{5} - \frac{3}{4} }= x^{\frac{-31}{20}}\\=\frac{1}{\sqrt[20]{ x^{31} }}\\=\frac{1}{|x|.\sqrt[20]{ x^{11} }}=\frac{1}{|x|.\sqrt[20]{ x^{11} }} \color{purple}{\frac{\sqrt[20]{ x^{9} }}{\sqrt[20]{ x^{9} }}} \\=\frac{\sqrt[20]{ x^{9} }}{|x^{2}|}\\---------------\)
5. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{1}{5}}}\\= q^{ \frac{1}{2} - \frac{1}{5} }= q^{\frac{3}{10}}\\=\sqrt[10]{ q^{3} }\\---------------\)
6. \(\dfrac{x^{\frac{5}{4}}}{x^{1}}\\= x^{ \frac{5}{4} - 1 }= x^{\frac{1}{4}}\\=\sqrt[4]{ x }\\---------------\)
7. \(\dfrac{x^{\frac{-5}{2}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{-5}{2} - (\frac{-1}{3}) }= x^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ x^{13} }}\\=\frac{1}{|x^{2}|.\sqrt[6]{ x }}=\frac{1}{|x^{2}|.\sqrt[6]{ x }} \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x^{3}|}\\---------------\)
8. \(\dfrac{y^{1}}{y^{\frac{-1}{2}}}\\= y^{ 1 - (\frac{-1}{2}) }= y^{\frac{3}{2}}\\= \sqrt{ y^{3} } =|y|. \sqrt{ y } \\---------------\)
9. \(\dfrac{q^{1}}{q^{\frac{4}{5}}}\\= q^{ 1 - \frac{4}{5} }= q^{\frac{1}{5}}\\=\sqrt[5]{ q }\\---------------\)
10. \(\dfrac{y^{-1}}{y^{\frac{1}{2}}}\\= y^{ -1 - \frac{1}{2} }= y^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ y^{3} } }\\=\frac{1}{|y|. \sqrt{ y } }=\frac{1}{|y|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{2}|}\\---------------\)
11. \(\dfrac{y^{\frac{-1}{6}}}{y^{\frac{5}{4}}}\\= y^{ \frac{-1}{6} - \frac{5}{4} }= y^{\frac{-17}{12}}\\=\frac{1}{\sqrt[12]{ y^{17} }}\\=\frac{1}{|y|.\sqrt[12]{ y^{5} }}=\frac{1}{|y|.\sqrt[12]{ y^{5} }} \color{purple}{\frac{\sqrt[12]{ y^{7} }}{\sqrt[12]{ y^{7} }}} \\=\frac{\sqrt[12]{ y^{7} }}{|y^{2}|}\\---------------\)
12. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{1}{3} - (\frac{-1}{2}) }= a^{\frac{5}{6}}\\=\sqrt[6]{ a^{5} }\\---------------\)