Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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