Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{5}{4}}}{x^{\frac{-1}{5}}}\\= x^{ \frac{5}{4} - (\frac{-1}{5}) }= x^{\frac{29}{20}}\\=\sqrt[20]{ x^{29} }=|x|.\sqrt[20]{ x^{9} }\\---------------\)
2. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{1}{3}}}\\= y^{ \frac{-1}{2} - \frac{1}{3} }= y^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ y^{5} }}=\frac{1}{\sqrt[6]{ y^{5} }}. \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y|}\\---------------\)
3. \(\dfrac{y^{\frac{5}{2}}}{y^{\frac{3}{4}}}\\= y^{ \frac{5}{2} - \frac{3}{4} }= y^{\frac{7}{4}}\\=\sqrt[4]{ y^{7} }=|y|.\sqrt[4]{ y^{3} }\\---------------\)
4. \(\dfrac{a^{\frac{-3}{4}}}{a^{\frac{-3}{5}}}\\= a^{ \frac{-3}{4} - (\frac{-3}{5}) }= a^{\frac{-3}{20}}\\=\frac{1}{\sqrt[20]{ a^{3} }}=\frac{1}{\sqrt[20]{ a^{3} }}. \color{purple}{\frac{\sqrt[20]{ a^{17} }}{\sqrt[20]{ a^{17} }}} \\=\frac{\sqrt[20]{ a^{17} }}{|a|}\\---------------\)
5. \(\dfrac{x^{2}}{x^{2}}\\= x^{ 2 - 2 }= x^{0}\\=1\\---------------\)
6. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{1}{3} - (\frac{-2}{3}) }= q^{1}\\\\---------------\)
7. \(\dfrac{q^{\frac{4}{5}}}{q^{\frac{-2}{5}}}\\= q^{ \frac{4}{5} - (\frac{-2}{5}) }= q^{\frac{6}{5}}\\=\sqrt[5]{ q^{6} }=q.\sqrt[5]{ q }\\---------------\)
8. \(\dfrac{q^{\frac{-3}{2}}}{q^{\frac{-1}{6}}}\\= q^{ \frac{-3}{2} - (\frac{-1}{6}) }= q^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ q^{4} }}\\=\frac{1}{q.\sqrt[3]{ q }}=\frac{1}{q.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{2}}\\---------------\)
9. \(\dfrac{x^{\frac{-1}{3}}}{x^{-1}}\\= x^{ \frac{-1}{3} - (-1) }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
10. \(\dfrac{a^{\frac{1}{5}}}{a^{\frac{-5}{4}}}\\= a^{ \frac{1}{5} - (\frac{-5}{4}) }= a^{\frac{29}{20}}\\=\sqrt[20]{ a^{29} }=|a|.\sqrt[20]{ a^{9} }\\---------------\)
11. \(\dfrac{x^{\frac{-4}{3}}}{x^{\frac{3}{4}}}\\= x^{ \frac{-4}{3} - \frac{3}{4} }= x^{\frac{-25}{12}}\\=\frac{1}{\sqrt[12]{ x^{25} }}\\=\frac{1}{|x^{2}|.\sqrt[12]{ x }}=\frac{1}{|x^{2}|.\sqrt[12]{ x }} \color{purple}{\frac{\sqrt[12]{ x^{11} }}{\sqrt[12]{ x^{11} }}} \\=\frac{\sqrt[12]{ x^{11} }}{|x^{3}|}\\---------------\)
12. \(\dfrac{q^{\frac{-1}{6}}}{q^{\frac{-4}{5}}}\\= q^{ \frac{-1}{6} - (\frac{-4}{5}) }= q^{\frac{19}{30}}\\=\sqrt[30]{ q^{19} }\\---------------\)