Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-1}{5}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{-1}{5} - (\frac{-1}{2}) }= a^{\frac{3}{10}}\\=\sqrt[10]{ a^{3} }\\---------------\)
2. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{1}{2}}}\\= x^{ \frac{2}{3} - \frac{1}{2} }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
3. \(\dfrac{a^{\frac{-1}{2}}}{a^{-2}}\\= a^{ \frac{-1}{2} - (-2) }= a^{\frac{3}{2}}\\= \sqrt{ a^{3} } =|a|. \sqrt{ a } \\---------------\)
4. \(\dfrac{x^{\frac{1}{3}}}{x^{-1}}\\= x^{ \frac{1}{3} - (-1) }= x^{\frac{4}{3}}\\=\sqrt[3]{ x^{4} }=x.\sqrt[3]{ x }\\---------------\)
5. \(\dfrac{x^{\frac{3}{4}}}{x^{\frac{5}{3}}}\\= x^{ \frac{3}{4} - \frac{5}{3} }= x^{\frac{-11}{12}}\\=\frac{1}{\sqrt[12]{ x^{11} }}=\frac{1}{\sqrt[12]{ x^{11} }}. \color{purple}{\frac{\sqrt[12]{ x }}{\sqrt[12]{ x }}} \\=\frac{\sqrt[12]{ x }}{|x|}\\---------------\)
6. \(\dfrac{q^{\frac{4}{3}}}{q^{\frac{-4}{5}}}\\= q^{ \frac{4}{3} - (\frac{-4}{5}) }= q^{\frac{32}{15}}\\=\sqrt[15]{ q^{32} }=q^{2}.\sqrt[15]{ q^{2} }\\---------------\)
7. \(\dfrac{y^{\frac{4}{5}}}{y^{\frac{-4}{5}}}\\= y^{ \frac{4}{5} - (\frac{-4}{5}) }= y^{\frac{8}{5}}\\=\sqrt[5]{ y^{8} }=y.\sqrt[5]{ y^{3} }\\---------------\)
8. \(\dfrac{q^{\frac{-4}{5}}}{q^{\frac{1}{2}}}\\= q^{ \frac{-4}{5} - \frac{1}{2} }= q^{\frac{-13}{10}}\\=\frac{1}{\sqrt[10]{ q^{13} }}\\=\frac{1}{|q|.\sqrt[10]{ q^{3} }}=\frac{1}{|q|.\sqrt[10]{ q^{3} }} \color{purple}{\frac{\sqrt[10]{ q^{7} }}{\sqrt[10]{ q^{7} }}} \\=\frac{\sqrt[10]{ q^{7} }}{|q^{2}|}\\---------------\)
9. \(\dfrac{q^{1}}{q^{\frac{3}{4}}}\\= q^{ 1 - \frac{3}{4} }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
10. \(\dfrac{a^{\frac{-5}{2}}}{a^{\frac{-4}{3}}}\\= a^{ \frac{-5}{2} - (\frac{-4}{3}) }= a^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ a^{7} }}\\=\frac{1}{|a|.\sqrt[6]{ a }}=\frac{1}{|a|.\sqrt[6]{ a }} \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a^{2}|}\\---------------\)
11. \(\dfrac{a^{\frac{-1}{4}}}{a^{-1}}\\= a^{ \frac{-1}{4} - (-1) }= a^{\frac{3}{4}}\\=\sqrt[4]{ a^{3} }\\---------------\)
12. \(\dfrac{x^{\frac{-5}{3}}}{x^{\frac{5}{3}}}\\= x^{ \frac{-5}{3} - \frac{5}{3} }= x^{\frac{-10}{3}}\\=\frac{1}{\sqrt[3]{ x^{10} }}\\=\frac{1}{x^{3}.\sqrt[3]{ x }}=\frac{1}{x^{3}.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{4}}\\---------------\)