Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{2}}{a^{1}}\\= a^{ 2 - 1 }= a^{1}\\\\---------------\)
2. \(\dfrac{y^{\frac{-3}{4}}}{y^{1}}\\= y^{ \frac{-3}{4} - 1 }= y^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[4]{ y^{3} }}=\frac{1}{|y|.\sqrt[4]{ y^{3} }} \color{purple}{\frac{\sqrt[4]{ y }}{\sqrt[4]{ y }}} \\=\frac{\sqrt[4]{ y }}{|y^{2}|}\\---------------\)
3. \(\dfrac{q^{\frac{-3}{5}}}{q^{\frac{-5}{3}}}\\= q^{ \frac{-3}{5} - (\frac{-5}{3}) }= q^{\frac{16}{15}}\\=\sqrt[15]{ q^{16} }=q.\sqrt[15]{ q }\\---------------\)
4. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{-5}{2}}}\\= a^{ \frac{-1}{2} - (\frac{-5}{2}) }= a^{2}\\\\---------------\)
5. \(\dfrac{y^{\frac{-5}{2}}}{y^{\frac{5}{4}}}\\= y^{ \frac{-5}{2} - \frac{5}{4} }= y^{\frac{-15}{4}}\\=\frac{1}{\sqrt[4]{ y^{15} }}\\=\frac{1}{|y^{3}|.\sqrt[4]{ y^{3} }}=\frac{1}{|y^{3}|.\sqrt[4]{ y^{3} }} \color{purple}{\frac{\sqrt[4]{ y }}{\sqrt[4]{ y }}} \\=\frac{\sqrt[4]{ y }}{|y^{4}|}\\---------------\)
6. \(\dfrac{a^{\frac{3}{4}}}{a^{\frac{5}{4}}}\\= a^{ \frac{3}{4} - \frac{5}{4} }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
7. \(\dfrac{y^{\frac{5}{4}}}{y^{\frac{-3}{5}}}\\= y^{ \frac{5}{4} - (\frac{-3}{5}) }= y^{\frac{37}{20}}\\=\sqrt[20]{ y^{37} }=|y|.\sqrt[20]{ y^{17} }\\---------------\)
8. \(\dfrac{q^{\frac{3}{5}}}{q^{\frac{1}{2}}}\\= q^{ \frac{3}{5} - \frac{1}{2} }= q^{\frac{1}{10}}\\=\sqrt[10]{ q }\\---------------\)
9. \(\dfrac{a^{\frac{4}{3}}}{a^{\frac{-1}{4}}}\\= a^{ \frac{4}{3} - (\frac{-1}{4}) }= a^{\frac{19}{12}}\\=\sqrt[12]{ a^{19} }=|a|.\sqrt[12]{ a^{7} }\\---------------\)
10. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{-1}{6}}}\\= y^{ \frac{-1}{3} - (\frac{-1}{6}) }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
11. \(\dfrac{y^{-2}}{y^{\frac{-5}{6}}}\\= y^{ -2 - (\frac{-5}{6}) }= y^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[6]{ y }}=\frac{1}{|y|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{2}|}\\---------------\)
12. \(\dfrac{a^{\frac{1}{5}}}{a^{\frac{-3}{5}}}\\= a^{ \frac{1}{5} - (\frac{-3}{5}) }= a^{\frac{4}{5}}\\=\sqrt[5]{ a^{4} }\\---------------\)