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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{1}{5}}}{a^{\frac{1}{2}}}\\= a^{ \frac{1}{5} - \frac{1}{2} }= a^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ a^{3} }}=\frac{1}{\sqrt[10]{ a^{3} }}. \color{purple}{\frac{\sqrt[10]{ a^{7} }}{\sqrt[10]{ a^{7} }}} \\=\frac{\sqrt[10]{ a^{7} }}{|a|}\\---------------\)
2. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{5}{2}}}\\= a^{ \frac{1}{2} - \frac{5}{2} }= a^{-2}\\=\frac{1}{a^{2}}\\---------------\)
3. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{2}{3} - (\frac{-2}{3}) }= a^{\frac{4}{3}}\\=\sqrt[3]{ a^{4} }=a.\sqrt[3]{ a }\\---------------\)
4. \(\dfrac{x^{\frac{-2}{5}}}{x^{\frac{-2}{3}}}\\= x^{ \frac{-2}{5} - (\frac{-2}{3}) }= x^{\frac{4}{15}}\\=\sqrt[15]{ x^{4} }\\---------------\)
5. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{-1}{6}}}\\= q^{ \frac{1}{2} - (\frac{-1}{6}) }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
6. \(\dfrac{q^{\frac{-5}{6}}}{q^{\frac{5}{2}}}\\= q^{ \frac{-5}{6} - \frac{5}{2} }= q^{\frac{-10}{3}}\\=\frac{1}{\sqrt[3]{ q^{10} }}\\=\frac{1}{q^{3}.\sqrt[3]{ q }}=\frac{1}{q^{3}.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{4}}\\---------------\)
7. \(\dfrac{x^{-2}}{x^{\frac{1}{5}}}\\= x^{ -2 - \frac{1}{5} }= x^{\frac{-11}{5}}\\=\frac{1}{\sqrt[5]{ x^{11} }}\\=\frac{1}{x^{2}.\sqrt[5]{ x }}=\frac{1}{x^{2}.\sqrt[5]{ x }} \color{purple}{\frac{\sqrt[5]{ x^{4} }}{\sqrt[5]{ x^{4} }}} \\=\frac{\sqrt[5]{ x^{4} }}{x^{3}}\\---------------\)
8. \(\dfrac{a^{\frac{-5}{3}}}{a^{\frac{-1}{5}}}\\= a^{ \frac{-5}{3} - (\frac{-1}{5}) }= a^{\frac{-22}{15}}\\=\frac{1}{\sqrt[15]{ a^{22} }}\\=\frac{1}{a.\sqrt[15]{ a^{7} }}=\frac{1}{a.\sqrt[15]{ a^{7} }} \color{purple}{\frac{\sqrt[15]{ a^{8} }}{\sqrt[15]{ a^{8} }}} \\=\frac{\sqrt[15]{ a^{8} }}{a^{2}}\\---------------\)
9. \(\dfrac{a^{\frac{4}{5}}}{a^{\frac{1}{5}}}\\= a^{ \frac{4}{5} - \frac{1}{5} }= a^{\frac{3}{5}}\\=\sqrt[5]{ a^{3} }\\---------------\)
10. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{-1}{5}}}\\= x^{ \frac{2}{3} - (\frac{-1}{5}) }= x^{\frac{13}{15}}\\=\sqrt[15]{ x^{13} }\\---------------\)
11. \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{2}{5}}}\\= x^{ \frac{-2}{3} - \frac{2}{5} }= x^{\frac{-16}{15}}\\=\frac{1}{\sqrt[15]{ x^{16} }}\\=\frac{1}{x.\sqrt[15]{ x }}=\frac{1}{x.\sqrt[15]{ x }} \color{purple}{\frac{\sqrt[15]{ x^{14} }}{\sqrt[15]{ x^{14} }}} \\=\frac{\sqrt[15]{ x^{14} }}{x^{2}}\\---------------\)
12. \(\dfrac{q^{\frac{5}{4}}}{q^{2}}\\= q^{ \frac{5}{4} - 2 }= q^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ q^{3} }}=\frac{1}{\sqrt[4]{ q^{3} }}. \color{purple}{\frac{\sqrt[4]{ q }}{\sqrt[4]{ q }}} \\=\frac{\sqrt[4]{ q }}{|q|}\\---------------\)