Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{1}}{y^{\frac{5}{4}}}\\= y^{ 1 - \frac{5}{4} }= y^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ y }}=\frac{1}{\sqrt[4]{ y }}. \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y|}\\---------------\)
2. \(\dfrac{y^{\frac{5}{2}}}{y^{\frac{-4}{3}}}\\= y^{ \frac{5}{2} - (\frac{-4}{3}) }= y^{\frac{23}{6}}\\=\sqrt[6]{ y^{23} }=|y^{3}|.\sqrt[6]{ y^{5} }\\---------------\)
3. \(\dfrac{q^{-1}}{q^{\frac{2}{5}}}\\= q^{ -1 - \frac{2}{5} }= q^{\frac{-7}{5}}\\=\frac{1}{\sqrt[5]{ q^{7} }}\\=\frac{1}{q.\sqrt[5]{ q^{2} }}=\frac{1}{q.\sqrt[5]{ q^{2} }} \color{purple}{\frac{\sqrt[5]{ q^{3} }}{\sqrt[5]{ q^{3} }}} \\=\frac{\sqrt[5]{ q^{3} }}{q^{2}}\\---------------\)
4. \(\dfrac{q^{\frac{1}{6}}}{q^{\frac{-3}{2}}}\\= q^{ \frac{1}{6} - (\frac{-3}{2}) }= q^{\frac{5}{3}}\\=\sqrt[3]{ q^{5} }=q.\sqrt[3]{ q^{2} }\\---------------\)
5. \(\dfrac{x^{\frac{2}{3}}}{x^{-1}}\\= x^{ \frac{2}{3} - (-1) }= x^{\frac{5}{3}}\\=\sqrt[3]{ x^{5} }=x.\sqrt[3]{ x^{2} }\\---------------\)
6. \(\dfrac{q^{-1}}{q^{\frac{-4}{3}}}\\= q^{ -1 - (\frac{-4}{3}) }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
7. \(\dfrac{a^{1}}{a^{\frac{-2}{5}}}\\= a^{ 1 - (\frac{-2}{5}) }= a^{\frac{7}{5}}\\=\sqrt[5]{ a^{7} }=a.\sqrt[5]{ a^{2} }\\---------------\)
8. \(\dfrac{a^{\frac{-1}{5}}}{a^{\frac{3}{5}}}\\= a^{ \frac{-1}{5} - \frac{3}{5} }= a^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ a^{4} }}=\frac{1}{\sqrt[5]{ a^{4} }}. \color{purple}{\frac{\sqrt[5]{ a }}{\sqrt[5]{ a }}} \\=\frac{\sqrt[5]{ a }}{a}\\---------------\)
9. \(\dfrac{x^{\frac{3}{5}}}{x^{\frac{4}{5}}}\\= x^{ \frac{3}{5} - \frac{4}{5} }= x^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ x }}=\frac{1}{\sqrt[5]{ x }}. \color{purple}{\frac{\sqrt[5]{ x^{4} }}{\sqrt[5]{ x^{4} }}} \\=\frac{\sqrt[5]{ x^{4} }}{x}\\---------------\)
10. \(\dfrac{q^{\frac{2}{5}}}{q^{\frac{-1}{6}}}\\= q^{ \frac{2}{5} - (\frac{-1}{6}) }= q^{\frac{17}{30}}\\=\sqrt[30]{ q^{17} }\\---------------\)
11. \(\dfrac{x^{\frac{5}{4}}}{x^{\frac{-5}{4}}}\\= x^{ \frac{5}{4} - (\frac{-5}{4}) }= x^{\frac{5}{2}}\\= \sqrt{ x^{5} } =|x^{2}|. \sqrt{ x } \\---------------\)
12. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{5}{3}}}\\= q^{ \frac{-2}{3} - \frac{5}{3} }= q^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ q^{7} }}\\=\frac{1}{q^{2}.\sqrt[3]{ q }}=\frac{1}{q^{2}.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{3}}\\---------------\)