Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-4}{3}}}{a^{1}}\\= a^{ \frac{-4}{3} - 1 }= a^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ a^{7} }}\\=\frac{1}{a^{2}.\sqrt[3]{ a }}=\frac{1}{a^{2}.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{3}}\\---------------\)
2. \(\dfrac{a^{\frac{5}{3}}}{a^{\frac{3}{4}}}\\= a^{ \frac{5}{3} - \frac{3}{4} }= a^{\frac{11}{12}}\\=\sqrt[12]{ a^{11} }\\---------------\)
3. \(\dfrac{a^{\frac{5}{3}}}{a^{\frac{-1}{6}}}\\= a^{ \frac{5}{3} - (\frac{-1}{6}) }= a^{\frac{11}{6}}\\=\sqrt[6]{ a^{11} }=|a|.\sqrt[6]{ a^{5} }\\---------------\)
4. \(\dfrac{a^{\frac{4}{5}}}{a^{\frac{-3}{5}}}\\= a^{ \frac{4}{5} - (\frac{-3}{5}) }= a^{\frac{7}{5}}\\=\sqrt[5]{ a^{7} }=a.\sqrt[5]{ a^{2} }\\---------------\)
5. \(\dfrac{x^{\frac{5}{4}}}{x^{1}}\\= x^{ \frac{5}{4} - 1 }= x^{\frac{1}{4}}\\=\sqrt[4]{ x }\\---------------\)
6. \(\dfrac{a^{\frac{-1}{3}}}{a^{-2}}\\= a^{ \frac{-1}{3} - (-2) }= a^{\frac{5}{3}}\\=\sqrt[3]{ a^{5} }=a.\sqrt[3]{ a^{2} }\\---------------\)
7. \(\dfrac{q^{\frac{-1}{2}}}{q^{1}}\\= q^{ \frac{-1}{2} - 1 }= q^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ q^{3} } }\\=\frac{1}{|q|. \sqrt{ q } }=\frac{1}{|q|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{2}|}\\---------------\)
8. \(\dfrac{x^{-1}}{x^{\frac{1}{3}}}\\= x^{ -1 - \frac{1}{3} }= x^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ x^{4} }}\\=\frac{1}{x.\sqrt[3]{ x }}=\frac{1}{x.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{2}}\\---------------\)
9. \(\dfrac{y^{\frac{1}{3}}}{y^{-1}}\\= y^{ \frac{1}{3} - (-1) }= y^{\frac{4}{3}}\\=\sqrt[3]{ y^{4} }=y.\sqrt[3]{ y }\\---------------\)
10. \(\dfrac{y^{\frac{-1}{6}}}{y^{-1}}\\= y^{ \frac{-1}{6} - (-1) }= y^{\frac{5}{6}}\\=\sqrt[6]{ y^{5} }\\---------------\)
11. \(\dfrac{a^{\frac{-5}{2}}}{a^{\frac{4}{3}}}\\= a^{ \frac{-5}{2} - \frac{4}{3} }= a^{\frac{-23}{6}}\\=\frac{1}{\sqrt[6]{ a^{23} }}\\=\frac{1}{|a^{3}|.\sqrt[6]{ a^{5} }}=\frac{1}{|a^{3}|.\sqrt[6]{ a^{5} }} \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a^{4}|}\\---------------\)
12. \(\dfrac{x^{\frac{1}{5}}}{x^{\frac{-3}{2}}}\\= x^{ \frac{1}{5} - (\frac{-3}{2}) }= x^{\frac{17}{10}}\\=\sqrt[10]{ x^{17} }=|x|.\sqrt[10]{ x^{7} }\\---------------\)