Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-5}{2}}}{x^{\frac{1}{6}}}\\= x^{ \frac{-5}{2} - \frac{1}{6} }= x^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ x^{8} }}\\=\frac{1}{x^{2}.\sqrt[3]{ x^{2} }}=\frac{1}{x^{2}.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{3}}\\---------------\)
2. \(\dfrac{q^{\frac{-5}{3}}}{q^{\frac{-1}{6}}}\\= q^{ \frac{-5}{3} - (\frac{-1}{6}) }= q^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ q^{3} } }\\=\frac{1}{|q|. \sqrt{ q } }=\frac{1}{|q|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{2}|}\\---------------\)
3. \(\dfrac{y^{\frac{-1}{5}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{-1}{5} - (\frac{-1}{2}) }= y^{\frac{3}{10}}\\=\sqrt[10]{ y^{3} }\\---------------\)
4. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{-5}{3}}}\\= a^{ \frac{-2}{3} - (\frac{-5}{3}) }= a^{1}\\\\---------------\)
5. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{1}{5}}}\\= y^{ \frac{1}{2} - \frac{1}{5} }= y^{\frac{3}{10}}\\=\sqrt[10]{ y^{3} }\\---------------\)
6. \(\dfrac{x^{\frac{-1}{4}}}{x^{\frac{4}{3}}}\\= x^{ \frac{-1}{4} - \frac{4}{3} }= x^{\frac{-19}{12}}\\=\frac{1}{\sqrt[12]{ x^{19} }}\\=\frac{1}{|x|.\sqrt[12]{ x^{7} }}=\frac{1}{|x|.\sqrt[12]{ x^{7} }} \color{purple}{\frac{\sqrt[12]{ x^{5} }}{\sqrt[12]{ x^{5} }}} \\=\frac{\sqrt[12]{ x^{5} }}{|x^{2}|}\\---------------\)
7. \(\dfrac{y^{\frac{3}{5}}}{y^{\frac{3}{5}}}\\= y^{ \frac{3}{5} - \frac{3}{5} }= y^{0}\\=1\\---------------\)
8. \(\dfrac{a^{\frac{5}{2}}}{a^{\frac{-4}{5}}}\\= a^{ \frac{5}{2} - (\frac{-4}{5}) }= a^{\frac{33}{10}}\\=\sqrt[10]{ a^{33} }=|a^{3}|.\sqrt[10]{ a^{3} }\\---------------\)
9. \(\dfrac{a^{\frac{-4}{5}}}{a^{\frac{1}{2}}}\\= a^{ \frac{-4}{5} - \frac{1}{2} }= a^{\frac{-13}{10}}\\=\frac{1}{\sqrt[10]{ a^{13} }}\\=\frac{1}{|a|.\sqrt[10]{ a^{3} }}=\frac{1}{|a|.\sqrt[10]{ a^{3} }} \color{purple}{\frac{\sqrt[10]{ a^{7} }}{\sqrt[10]{ a^{7} }}} \\=\frac{\sqrt[10]{ a^{7} }}{|a^{2}|}\\---------------\)
10. \(\dfrac{q^{\frac{4}{3}}}{q^{\frac{2}{3}}}\\= q^{ \frac{4}{3} - \frac{2}{3} }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
11. \(\dfrac{y^{\frac{-5}{3}}}{y^{\frac{1}{2}}}\\= y^{ \frac{-5}{3} - \frac{1}{2} }= y^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ y^{13} }}\\=\frac{1}{|y^{2}|.\sqrt[6]{ y }}=\frac{1}{|y^{2}|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{3}|}\\---------------\)
12. \(\dfrac{q^{\frac{-2}{5}}}{q^{1}}\\= q^{ \frac{-2}{5} - 1 }= q^{\frac{-7}{5}}\\=\frac{1}{\sqrt[5]{ q^{7} }}\\=\frac{1}{q.\sqrt[5]{ q^{2} }}=\frac{1}{q.\sqrt[5]{ q^{2} }} \color{purple}{\frac{\sqrt[5]{ q^{3} }}{\sqrt[5]{ q^{3} }}} \\=\frac{\sqrt[5]{ q^{3} }}{q^{2}}\\---------------\)