Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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