Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{-1}}{q^{\frac{1}{2}}}\\= q^{ -1 - \frac{1}{2} }= q^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ q^{3} } }\\=\frac{1}{|q|. \sqrt{ q } }=\frac{1}{|q|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{2}|}\\---------------\)
2. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{-5}{3}}}\\= q^{ \frac{1}{3} - (\frac{-5}{3}) }= q^{2}\\\\---------------\)
3. \(\dfrac{y^{-1}}{y^{\frac{5}{6}}}\\= y^{ -1 - \frac{5}{6} }= y^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ y^{11} }}\\=\frac{1}{|y|.\sqrt[6]{ y^{5} }}=\frac{1}{|y|.\sqrt[6]{ y^{5} }} \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y^{2}|}\\---------------\)
4. \(\dfrac{q^{1}}{q^{\frac{-1}{5}}}\\= q^{ 1 - (\frac{-1}{5}) }= q^{\frac{6}{5}}\\=\sqrt[5]{ q^{6} }=q.\sqrt[5]{ q }\\---------------\)
5. \(\dfrac{x^{-1}}{x^{\frac{-1}{6}}}\\= x^{ -1 - (\frac{-1}{6}) }= x^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ x^{5} }}=\frac{1}{\sqrt[6]{ x^{5} }}. \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x|}\\---------------\)
6. \(\dfrac{y^{1}}{y^{-1}}\\= y^{ 1 - (-1) }= y^{2}\\\\---------------\)
7. \(\dfrac{a^{1}}{a^{\frac{-3}{5}}}\\= a^{ 1 - (\frac{-3}{5}) }= a^{\frac{8}{5}}\\=\sqrt[5]{ a^{8} }=a.\sqrt[5]{ a^{3} }\\---------------\)
8. \(\dfrac{x^{\frac{-3}{5}}}{x^{\frac{-2}{3}}}\\= x^{ \frac{-3}{5} - (\frac{-2}{3}) }= x^{\frac{1}{15}}\\=\sqrt[15]{ x }\\---------------\)
9. \(\dfrac{q^{1}}{q^{\frac{-1}{2}}}\\= q^{ 1 - (\frac{-1}{2}) }= q^{\frac{3}{2}}\\= \sqrt{ q^{3} } =|q|. \sqrt{ q } \\---------------\)
10. \(\dfrac{y^{\frac{5}{4}}}{y^{\frac{3}{2}}}\\= y^{ \frac{5}{4} - \frac{3}{2} }= y^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ y }}=\frac{1}{\sqrt[4]{ y }}. \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y|}\\---------------\)
11. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{5}{6}}}\\= x^{ \frac{1}{2} - \frac{5}{6} }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
12. \(\dfrac{a^{\frac{2}{5}}}{a^{\frac{-5}{4}}}\\= a^{ \frac{2}{5} - (\frac{-5}{4}) }= a^{\frac{33}{20}}\\=\sqrt[20]{ a^{33} }=|a|.\sqrt[20]{ a^{13} }\\---------------\)