Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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