Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{5}{3}}}{y^{\frac{-4}{5}}}\\= y^{ \frac{5}{3} - (\frac{-4}{5}) }= y^{\frac{37}{15}}\\=\sqrt[15]{ y^{37} }=y^{2}.\sqrt[15]{ y^{7} }\\---------------\)
2. \(\dfrac{a^{2}}{a^{\frac{1}{6}}}\\= a^{ 2 - \frac{1}{6} }= a^{\frac{11}{6}}\\=\sqrt[6]{ a^{11} }=|a|.\sqrt[6]{ a^{5} }\\---------------\)
3. \(\dfrac{x^{\frac{-2}{5}}}{x^{-1}}\\= x^{ \frac{-2}{5} - (-1) }= x^{\frac{3}{5}}\\=\sqrt[5]{ x^{3} }\\---------------\)
4. \(\dfrac{x^{\frac{4}{3}}}{x^{\frac{5}{6}}}\\= x^{ \frac{4}{3} - \frac{5}{6} }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
5. \(\dfrac{a^{\frac{5}{4}}}{a^{\frac{-2}{5}}}\\= a^{ \frac{5}{4} - (\frac{-2}{5}) }= a^{\frac{33}{20}}\\=\sqrt[20]{ a^{33} }=|a|.\sqrt[20]{ a^{13} }\\---------------\)
6. \(\dfrac{q^{\frac{-5}{3}}}{q^{\frac{2}{5}}}\\= q^{ \frac{-5}{3} - \frac{2}{5} }= q^{\frac{-31}{15}}\\=\frac{1}{\sqrt[15]{ q^{31} }}\\=\frac{1}{q^{2}.\sqrt[15]{ q }}=\frac{1}{q^{2}.\sqrt[15]{ q }} \color{purple}{\frac{\sqrt[15]{ q^{14} }}{\sqrt[15]{ q^{14} }}} \\=\frac{\sqrt[15]{ q^{14} }}{q^{3}}\\---------------\)
7. \(\dfrac{x^{-2}}{x^{\frac{2}{3}}}\\= x^{ -2 - \frac{2}{3} }= x^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ x^{8} }}\\=\frac{1}{x^{2}.\sqrt[3]{ x^{2} }}=\frac{1}{x^{2}.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{3}}\\---------------\)
8. \(\dfrac{y^{\frac{-1}{2}}}{y^{2}}\\= y^{ \frac{-1}{2} - 2 }= y^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ y^{5} } }\\=\frac{1}{|y^{2}|. \sqrt{ y } }=\frac{1}{|y^{2}|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{3}|}\\---------------\)
9. \(\dfrac{q^{-1}}{q^{\frac{-5}{3}}}\\= q^{ -1 - (\frac{-5}{3}) }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
10. \(\dfrac{x^{\frac{-3}{5}}}{x^{1}}\\= x^{ \frac{-3}{5} - 1 }= x^{\frac{-8}{5}}\\=\frac{1}{\sqrt[5]{ x^{8} }}\\=\frac{1}{x.\sqrt[5]{ x^{3} }}=\frac{1}{x.\sqrt[5]{ x^{3} }} \color{purple}{\frac{\sqrt[5]{ x^{2} }}{\sqrt[5]{ x^{2} }}} \\=\frac{\sqrt[5]{ x^{2} }}{x^{2}}\\---------------\)
11. \(\dfrac{x^{1}}{x^{\frac{-1}{5}}}\\= x^{ 1 - (\frac{-1}{5}) }= x^{\frac{6}{5}}\\=\sqrt[5]{ x^{6} }=x.\sqrt[5]{ x }\\---------------\)
12. \(\dfrac{x^{\frac{1}{4}}}{x^{\frac{-1}{4}}}\\= x^{ \frac{1}{4} - (\frac{-1}{4}) }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)