Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{1}{6}}}{a^{\frac{1}{2}}}\\= a^{ \frac{1}{6} - \frac{1}{2} }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
2. \(\dfrac{q^{\frac{5}{6}}}{q^{\frac{5}{4}}}\\= q^{ \frac{5}{6} - \frac{5}{4} }= q^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ q^{5} }}=\frac{1}{\sqrt[12]{ q^{5} }}. \color{purple}{\frac{\sqrt[12]{ q^{7} }}{\sqrt[12]{ q^{7} }}} \\=\frac{\sqrt[12]{ q^{7} }}{|q|}\\---------------\)
3. \(\dfrac{x^{\frac{-5}{6}}}{x^{-1}}\\= x^{ \frac{-5}{6} - (-1) }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
4. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{1}{6}}}\\= a^{ \frac{-1}{3} - \frac{1}{6} }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
5. \(\dfrac{x^{\frac{4}{5}}}{x^{-1}}\\= x^{ \frac{4}{5} - (-1) }= x^{\frac{9}{5}}\\=\sqrt[5]{ x^{9} }=x.\sqrt[5]{ x^{4} }\\---------------\)
6. \(\dfrac{y^{\frac{-1}{5}}}{y^{\frac{-3}{2}}}\\= y^{ \frac{-1}{5} - (\frac{-3}{2}) }= y^{\frac{13}{10}}\\=\sqrt[10]{ y^{13} }=|y|.\sqrt[10]{ y^{3} }\\---------------\)
7. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{1}{2}}}\\= y^{ \frac{1}{2} - \frac{1}{2} }= y^{0}\\=1\\---------------\)
8. \(\dfrac{q^{1}}{q^{\frac{3}{2}}}\\= q^{ 1 - \frac{3}{2} }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
9. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{-4}{5}}}\\= q^{ \frac{2}{3} - (\frac{-4}{5}) }= q^{\frac{22}{15}}\\=\sqrt[15]{ q^{22} }=q.\sqrt[15]{ q^{7} }\\---------------\)
10. \(\dfrac{x^{\frac{5}{2}}}{x^{\frac{-3}{4}}}\\= x^{ \frac{5}{2} - (\frac{-3}{4}) }= x^{\frac{13}{4}}\\=\sqrt[4]{ x^{13} }=|x^{3}|.\sqrt[4]{ x }\\---------------\)
11. \(\dfrac{x^{\frac{-4}{3}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{-4}{3} - (\frac{-1}{3}) }= x^{-1}\\=\frac{1}{x}\\---------------\)
12. \(\dfrac{x^{-1}}{x^{-1}}\\= x^{ -1 - (-1) }= x^{0}\\=1\\---------------\)