Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{1}{4}}}{x^{\frac{1}{4}}}\\= x^{ \frac{1}{4} - \frac{1}{4} }= x^{0}\\=1\\---------------\)
2. \(\dfrac{x^{\frac{-3}{2}}}{x^{\frac{-2}{3}}}\\= x^{ \frac{-3}{2} - (\frac{-2}{3}) }= x^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ x^{5} }}=\frac{1}{\sqrt[6]{ x^{5} }}. \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x|}\\---------------\)
3. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{5}{3}}}\\= q^{ \frac{-1}{3} - \frac{5}{3} }= q^{-2}\\=\frac{1}{q^{2}}\\---------------\)
4. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{1}{2} - (\frac{-1}{2}) }= y^{1}\\\\---------------\)
5. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{-1}{2} - (\frac{-1}{3}) }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
6. \(\dfrac{x^{1}}{x^{\frac{1}{3}}}\\= x^{ 1 - \frac{1}{3} }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
7. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{-1}{2} - (\frac{-2}{3}) }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)
8. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{-1}{2} - (\frac{-1}{2}) }= a^{0}\\=1\\---------------\)
9. \(\dfrac{y^{\frac{1}{5}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{1}{5} - (\frac{-1}{2}) }= y^{\frac{7}{10}}\\=\sqrt[10]{ y^{7} }\\---------------\)
10. \(\dfrac{q^{\frac{-2}{5}}}{q^{\frac{-5}{2}}}\\= q^{ \frac{-2}{5} - (\frac{-5}{2}) }= q^{\frac{21}{10}}\\=\sqrt[10]{ q^{21} }=|q^{2}|.\sqrt[10]{ q }\\---------------\)
11. \(\dfrac{q^{\frac{5}{6}}}{q^{1}}\\= q^{ \frac{5}{6} - 1 }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)
12. \(\dfrac{q^{\frac{-5}{2}}}{q^{-1}}\\= q^{ \frac{-5}{2} - (-1) }= q^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ q^{3} } }\\=\frac{1}{|q|. \sqrt{ q } }=\frac{1}{|q|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{2}|}\\---------------\)