Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{1}{4}}}{q^{\frac{1}{3}}}\\= q^{ \frac{1}{4} - \frac{1}{3} }= q^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ q }}=\frac{1}{\sqrt[12]{ q }}. \color{purple}{\frac{\sqrt[12]{ q^{11} }}{\sqrt[12]{ q^{11} }}} \\=\frac{\sqrt[12]{ q^{11} }}{|q|}\\---------------\)
2. \(\dfrac{q^{1}}{q^{\frac{-5}{4}}}\\= q^{ 1 - (\frac{-5}{4}) }= q^{\frac{9}{4}}\\=\sqrt[4]{ q^{9} }=|q^{2}|.\sqrt[4]{ q }\\---------------\)
3. \(\dfrac{a^{\frac{-2}{5}}}{a^{\frac{1}{2}}}\\= a^{ \frac{-2}{5} - \frac{1}{2} }= a^{\frac{-9}{10}}\\=\frac{1}{\sqrt[10]{ a^{9} }}=\frac{1}{\sqrt[10]{ a^{9} }}. \color{purple}{\frac{\sqrt[10]{ a }}{\sqrt[10]{ a }}} \\=\frac{\sqrt[10]{ a }}{|a|}\\---------------\)
4. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{-1}{3} - (\frac{-2}{3}) }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
5. \(\dfrac{x^{-2}}{x^{\frac{-1}{4}}}\\= x^{ -2 - (\frac{-1}{4}) }= x^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ x^{7} }}\\=\frac{1}{|x|.\sqrt[4]{ x^{3} }}=\frac{1}{|x|.\sqrt[4]{ x^{3} }} \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x^{2}|}\\---------------\)
6. \(\dfrac{q^{-1}}{q^{\frac{1}{2}}}\\= q^{ -1 - \frac{1}{2} }= q^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ q^{3} } }\\=\frac{1}{|q|. \sqrt{ q } }=\frac{1}{|q|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{2}|}\\---------------\)
7. \(\dfrac{x^{\frac{-5}{2}}}{x^{\frac{1}{5}}}\\= x^{ \frac{-5}{2} - \frac{1}{5} }= x^{\frac{-27}{10}}\\=\frac{1}{\sqrt[10]{ x^{27} }}\\=\frac{1}{|x^{2}|.\sqrt[10]{ x^{7} }}=\frac{1}{|x^{2}|.\sqrt[10]{ x^{7} }} \color{purple}{\frac{\sqrt[10]{ x^{3} }}{\sqrt[10]{ x^{3} }}} \\=\frac{\sqrt[10]{ x^{3} }}{|x^{3}|}\\---------------\)
8. \(\dfrac{a^{\frac{5}{3}}}{a^{\frac{5}{3}}}\\= a^{ \frac{5}{3} - \frac{5}{3} }= a^{0}\\=1\\---------------\)
9. \(\dfrac{y^{2}}{y^{\frac{-4}{3}}}\\= y^{ 2 - (\frac{-4}{3}) }= y^{\frac{10}{3}}\\=\sqrt[3]{ y^{10} }=y^{3}.\sqrt[3]{ y }\\---------------\)
10. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{1}{4}}}\\= x^{ \frac{-1}{3} - \frac{1}{4} }= x^{\frac{-7}{12}}\\=\frac{1}{\sqrt[12]{ x^{7} }}=\frac{1}{\sqrt[12]{ x^{7} }}. \color{purple}{\frac{\sqrt[12]{ x^{5} }}{\sqrt[12]{ x^{5} }}} \\=\frac{\sqrt[12]{ x^{5} }}{|x|}\\---------------\)
11. \(\dfrac{x^{1}}{x^{\frac{5}{6}}}\\= x^{ 1 - \frac{5}{6} }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
12. \(\dfrac{q^{1}}{q^{\frac{-1}{2}}}\\= q^{ 1 - (\frac{-1}{2}) }= q^{\frac{3}{2}}\\= \sqrt{ q^{3} } =|q|. \sqrt{ q } \\---------------\)