Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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