Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{1}{5}}}{x^{\frac{1}{3}}}\\= x^{ \frac{1}{5} - \frac{1}{3} }= x^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ x^{2} }}=\frac{1}{\sqrt[15]{ x^{2} }}. \color{purple}{\frac{\sqrt[15]{ x^{13} }}{\sqrt[15]{ x^{13} }}} \\=\frac{\sqrt[15]{ x^{13} }}{x}\\---------------\)
2. \(\dfrac{y^{\frac{5}{4}}}{y^{\frac{1}{3}}}\\= y^{ \frac{5}{4} - \frac{1}{3} }= y^{\frac{11}{12}}\\=\sqrt[12]{ y^{11} }\\---------------\)
3. \(\dfrac{a^{\frac{-3}{4}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{-3}{4} - (\frac{-1}{2}) }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
4. \(\dfrac{q^{\frac{-1}{5}}}{q^{\frac{1}{2}}}\\= q^{ \frac{-1}{5} - \frac{1}{2} }= q^{\frac{-7}{10}}\\=\frac{1}{\sqrt[10]{ q^{7} }}=\frac{1}{\sqrt[10]{ q^{7} }}. \color{purple}{\frac{\sqrt[10]{ q^{3} }}{\sqrt[10]{ q^{3} }}} \\=\frac{\sqrt[10]{ q^{3} }}{|q|}\\---------------\)
5. \(\dfrac{q^{\frac{1}{4}}}{q^{\frac{-4}{5}}}\\= q^{ \frac{1}{4} - (\frac{-4}{5}) }= q^{\frac{21}{20}}\\=\sqrt[20]{ q^{21} }=|q|.\sqrt[20]{ q }\\---------------\)
6. \(\dfrac{x^{1}}{x^{1}}\\= x^{ 1 - 1 }= x^{0}\\=1\\---------------\)
7. \(\dfrac{x^{\frac{3}{2}}}{x^{\frac{4}{5}}}\\= x^{ \frac{3}{2} - \frac{4}{5} }= x^{\frac{7}{10}}\\=\sqrt[10]{ x^{7} }\\---------------\)
8. \(\dfrac{q^{\frac{-5}{3}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{-5}{3} - (\frac{-1}{3}) }= q^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ q^{4} }}\\=\frac{1}{q.\sqrt[3]{ q }}=\frac{1}{q.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{2}}\\---------------\)
9. \(\dfrac{a^{-1}}{a^{\frac{4}{5}}}\\= a^{ -1 - \frac{4}{5} }= a^{\frac{-9}{5}}\\=\frac{1}{\sqrt[5]{ a^{9} }}\\=\frac{1}{a.\sqrt[5]{ a^{4} }}=\frac{1}{a.\sqrt[5]{ a^{4} }} \color{purple}{\frac{\sqrt[5]{ a }}{\sqrt[5]{ a }}} \\=\frac{\sqrt[5]{ a }}{a^{2}}\\---------------\)
10. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{-1}{2} - (\frac{-1}{3}) }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
11. \(\dfrac{q^{-1}}{q^{\frac{5}{6}}}\\= q^{ -1 - \frac{5}{6} }= q^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ q^{11} }}\\=\frac{1}{|q|.\sqrt[6]{ q^{5} }}=\frac{1}{|q|.\sqrt[6]{ q^{5} }} \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q^{2}|}\\---------------\)
12. \(\dfrac{q^{1}}{q^{-2}}\\= q^{ 1 - (-2) }= q^{3}\\\\---------------\)