Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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