Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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