Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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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. \(\dfrac{q^{1}}{q^{\frac{-1}{2}}}\\= q^{ 1 - (\frac{-1}{2}) }= q^{\frac{3}{2}}\\= \sqrt{ q^{3} } =|q|. \sqrt{ q } \\---------------\)
3. \(\dfrac{q^{1}}{q^{\frac{4}{3}}}\\= q^{ 1 - \frac{4}{3} }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
4. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{4}{3}}}\\= y^{ \frac{-1}{2} - \frac{4}{3} }= y^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ y^{11} }}\\=\frac{1}{|y|.\sqrt[6]{ y^{5} }}=\frac{1}{|y|.\sqrt[6]{ y^{5} }} \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y^{2}|}\\---------------\)
5. \(\dfrac{a^{-1}}{a^{\frac{3}{4}}}\\= a^{ -1 - \frac{3}{4} }= a^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ a^{7} }}\\=\frac{1}{|a|.\sqrt[4]{ a^{3} }}=\frac{1}{|a|.\sqrt[4]{ a^{3} }} \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a^{2}|}\\---------------\)
6. \(\dfrac{y^{\frac{-3}{5}}}{y^{\frac{3}{2}}}\\= y^{ \frac{-3}{5} - \frac{3}{2} }= y^{\frac{-21}{10}}\\=\frac{1}{\sqrt[10]{ y^{21} }}\\=\frac{1}{|y^{2}|.\sqrt[10]{ y }}=\frac{1}{|y^{2}|.\sqrt[10]{ y }} \color{purple}{\frac{\sqrt[10]{ y^{9} }}{\sqrt[10]{ y^{9} }}} \\=\frac{\sqrt[10]{ y^{9} }}{|y^{3}|}\\---------------\)
7. \(\dfrac{a^{\frac{-1}{4}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{-1}{4} - (\frac{-1}{2}) }= a^{\frac{1}{4}}\\=\sqrt[4]{ a }\\---------------\)
8. \(\dfrac{a^{1}}{a^{\frac{1}{2}}}\\= a^{ 1 - \frac{1}{2} }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
9. \(\dfrac{y^{\frac{-1}{2}}}{y^{2}}\\= y^{ \frac{-1}{2} - 2 }= y^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ y^{5} } }\\=\frac{1}{|y^{2}|. \sqrt{ y } }=\frac{1}{|y^{2}|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{3}|}\\---------------\)
10. \(\dfrac{y^{\frac{1}{4}}}{y^{1}}\\= y^{ \frac{1}{4} - 1 }= y^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ y^{3} }}=\frac{1}{\sqrt[4]{ y^{3} }}. \color{purple}{\frac{\sqrt[4]{ y }}{\sqrt[4]{ y }}} \\=\frac{\sqrt[4]{ y }}{|y|}\\---------------\)
11. \(\dfrac{a^{\frac{5}{3}}}{a^{\frac{-2}{5}}}\\= a^{ \frac{5}{3} - (\frac{-2}{5}) }= a^{\frac{31}{15}}\\=\sqrt[15]{ a^{31} }=a^{2}.\sqrt[15]{ a }\\---------------\)
12. \(\dfrac{y^{-2}}{y^{1}}\\= y^{ -2 - 1 }= y^{-3}\\=\frac{1}{y^{3}}\\---------------\)