Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{1}}{y^{\frac{-1}{3}}}\\= y^{ 1 - (\frac{-1}{3}) }= y^{\frac{4}{3}}\\=\sqrt[3]{ y^{4} }=y.\sqrt[3]{ y }\\---------------\)
2. \(\dfrac{x^{\frac{1}{2}}}{x^{2}}\\= x^{ \frac{1}{2} - 2 }= x^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ x^{3} } }\\=\frac{1}{|x|. \sqrt{ x } }=\frac{1}{|x|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{2}|}\\---------------\)
3. \(\dfrac{x^{\frac{-5}{6}}}{x^{\frac{5}{2}}}\\= x^{ \frac{-5}{6} - \frac{5}{2} }= x^{\frac{-10}{3}}\\=\frac{1}{\sqrt[3]{ x^{10} }}\\=\frac{1}{x^{3}.\sqrt[3]{ x }}=\frac{1}{x^{3}.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{4}}\\---------------\)
4. \(\dfrac{q^{\frac{-3}{2}}}{q^{\frac{-5}{2}}}\\= q^{ \frac{-3}{2} - (\frac{-5}{2}) }= q^{1}\\\\---------------\)
5. \(\dfrac{q^{\frac{-5}{2}}}{q^{\frac{-4}{5}}}\\= q^{ \frac{-5}{2} - (\frac{-4}{5}) }= q^{\frac{-17}{10}}\\=\frac{1}{\sqrt[10]{ q^{17} }}\\=\frac{1}{|q|.\sqrt[10]{ q^{7} }}=\frac{1}{|q|.\sqrt[10]{ q^{7} }} \color{purple}{\frac{\sqrt[10]{ q^{3} }}{\sqrt[10]{ q^{3} }}} \\=\frac{\sqrt[10]{ q^{3} }}{|q^{2}|}\\---------------\)
6. \(\dfrac{y^{\frac{2}{5}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{2}{5} - (\frac{-1}{2}) }= y^{\frac{9}{10}}\\=\sqrt[10]{ y^{9} }\\---------------\)
7. \(\dfrac{x^{\frac{5}{6}}}{x^{\frac{-1}{6}}}\\= x^{ \frac{5}{6} - (\frac{-1}{6}) }= x^{1}\\\\---------------\)
8. \(\dfrac{y^{\frac{3}{5}}}{y^{\frac{-1}{4}}}\\= y^{ \frac{3}{5} - (\frac{-1}{4}) }= y^{\frac{17}{20}}\\=\sqrt[20]{ y^{17} }\\---------------\)
9. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{-3}{5}}}\\= a^{ \frac{-1}{3} - (\frac{-3}{5}) }= a^{\frac{4}{15}}\\=\sqrt[15]{ a^{4} }\\---------------\)
10. \(\dfrac{y^{\frac{2}{3}}}{y^{1}}\\= y^{ \frac{2}{3} - 1 }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
11. \(\dfrac{a^{\frac{-1}{6}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{-1}{6} - (\frac{-2}{3}) }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
12. \(\dfrac{q^{-1}}{q^{\frac{-4}{5}}}\\= q^{ -1 - (\frac{-4}{5}) }= q^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ q }}=\frac{1}{\sqrt[5]{ q }}. \color{purple}{\frac{\sqrt[5]{ q^{4} }}{\sqrt[5]{ q^{4} }}} \\=\frac{\sqrt[5]{ q^{4} }}{q}\\---------------\)