Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-3}{5}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{-3}{5} - (\frac{-1}{2}) }= y^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ y }}=\frac{1}{\sqrt[10]{ y }}. \color{purple}{\frac{\sqrt[10]{ y^{9} }}{\sqrt[10]{ y^{9} }}} \\=\frac{\sqrt[10]{ y^{9} }}{|y|}\\---------------\)
2. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{-5}{6}}}\\= q^{ \frac{1}{2} - (\frac{-5}{6}) }= q^{\frac{4}{3}}\\=\sqrt[3]{ q^{4} }=q.\sqrt[3]{ q }\\---------------\)
3. \(\dfrac{y^{1}}{y^{-1}}\\= y^{ 1 - (-1) }= y^{2}\\\\---------------\)
4. \(\dfrac{y^{\frac{3}{4}}}{y^{-2}}\\= y^{ \frac{3}{4} - (-2) }= y^{\frac{11}{4}}\\=\sqrt[4]{ y^{11} }=|y^{2}|.\sqrt[4]{ y^{3} }\\---------------\)
5. \(\dfrac{x^{\frac{3}{5}}}{x^{\frac{-5}{3}}}\\= x^{ \frac{3}{5} - (\frac{-5}{3}) }= x^{\frac{34}{15}}\\=\sqrt[15]{ x^{34} }=x^{2}.\sqrt[15]{ x^{4} }\\---------------\)
6. \(\dfrac{x^{\frac{3}{4}}}{x^{\frac{-3}{2}}}\\= x^{ \frac{3}{4} - (\frac{-3}{2}) }= x^{\frac{9}{4}}\\=\sqrt[4]{ x^{9} }=|x^{2}|.\sqrt[4]{ x }\\---------------\)
7. \(\dfrac{y^{\frac{-1}{3}}}{y^{-1}}\\= y^{ \frac{-1}{3} - (-1) }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
8. \(\dfrac{a^{\frac{-2}{3}}}{a^{-1}}\\= a^{ \frac{-2}{3} - (-1) }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
9. \(\dfrac{x^{\frac{-5}{2}}}{x^{-1}}\\= x^{ \frac{-5}{2} - (-1) }= x^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ x^{3} } }\\=\frac{1}{|x|. \sqrt{ x } }=\frac{1}{|x|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{2}|}\\---------------\)
10. \(\dfrac{x^{\frac{5}{6}}}{x^{\frac{-2}{3}}}\\= x^{ \frac{5}{6} - (\frac{-2}{3}) }= x^{\frac{3}{2}}\\= \sqrt{ x^{3} } =|x|. \sqrt{ x } \\---------------\)
11. \(\dfrac{y^{\frac{-4}{5}}}{y^{\frac{3}{5}}}\\= y^{ \frac{-4}{5} - \frac{3}{5} }= y^{\frac{-7}{5}}\\=\frac{1}{\sqrt[5]{ y^{7} }}\\=\frac{1}{y.\sqrt[5]{ y^{2} }}=\frac{1}{y.\sqrt[5]{ y^{2} }} \color{purple}{\frac{\sqrt[5]{ y^{3} }}{\sqrt[5]{ y^{3} }}} \\=\frac{\sqrt[5]{ y^{3} }}{y^{2}}\\---------------\)
12. \(\dfrac{a^{\frac{-1}{5}}}{a^{\frac{1}{3}}}\\= a^{ \frac{-1}{5} - \frac{1}{3} }= a^{\frac{-8}{15}}\\=\frac{1}{\sqrt[15]{ a^{8} }}=\frac{1}{\sqrt[15]{ a^{8} }}. \color{purple}{\frac{\sqrt[15]{ a^{7} }}{\sqrt[15]{ a^{7} }}} \\=\frac{\sqrt[15]{ a^{7} }}{a}\\---------------\)