Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-3}{4}}}{y^{-1}}\\= y^{ \frac{-3}{4} - (-1) }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)
2. \(\dfrac{x^{\frac{-4}{3}}}{x^{\frac{-4}{3}}}\\= x^{ \frac{-4}{3} - (\frac{-4}{3}) }= x^{0}\\=1\\---------------\)
3. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{1}{2} - (\frac{-1}{3}) }= x^{\frac{5}{6}}\\=\sqrt[6]{ x^{5} }\\---------------\)
4. \(\dfrac{y^{\frac{1}{3}}}{y^{\frac{5}{2}}}\\= y^{ \frac{1}{3} - \frac{5}{2} }= y^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ y^{13} }}\\=\frac{1}{|y^{2}|.\sqrt[6]{ y }}=\frac{1}{|y^{2}|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{3}|}\\---------------\)
5. \(\dfrac{y^{\frac{1}{3}}}{y^{\frac{-5}{3}}}\\= y^{ \frac{1}{3} - (\frac{-5}{3}) }= y^{2}\\\\---------------\)
6. \(\dfrac{x^{\frac{2}{3}}}{x^{-1}}\\= x^{ \frac{2}{3} - (-1) }= x^{\frac{5}{3}}\\=\sqrt[3]{ x^{5} }=x.\sqrt[3]{ x^{2} }\\---------------\)
7. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{-3}{5}}}\\= y^{ \frac{-1}{3} - (\frac{-3}{5}) }= y^{\frac{4}{15}}\\=\sqrt[15]{ y^{4} }\\---------------\)
8. \(\dfrac{y^{\frac{1}{3}}}{y^{\frac{1}{5}}}\\= y^{ \frac{1}{3} - \frac{1}{5} }= y^{\frac{2}{15}}\\=\sqrt[15]{ y^{2} }\\---------------\)
9. \(\dfrac{y^{\frac{3}{2}}}{y^{-1}}\\= y^{ \frac{3}{2} - (-1) }= y^{\frac{5}{2}}\\= \sqrt{ y^{5} } =|y^{2}|. \sqrt{ y } \\---------------\)
10. \(\dfrac{q^{\frac{3}{4}}}{q^{\frac{1}{2}}}\\= q^{ \frac{3}{4} - \frac{1}{2} }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
11. \(\dfrac{x^{\frac{-4}{5}}}{x^{\frac{2}{5}}}\\= x^{ \frac{-4}{5} - \frac{2}{5} }= x^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ x^{6} }}\\=\frac{1}{x.\sqrt[5]{ x }}=\frac{1}{x.\sqrt[5]{ x }} \color{purple}{\frac{\sqrt[5]{ x^{4} }}{\sqrt[5]{ x^{4} }}} \\=\frac{\sqrt[5]{ x^{4} }}{x^{2}}\\---------------\)
12. \(\dfrac{a^{\frac{5}{3}}}{a^{\frac{-5}{2}}}\\= a^{ \frac{5}{3} - (\frac{-5}{2}) }= a^{\frac{25}{6}}\\=\sqrt[6]{ a^{25} }=|a^{4}|.\sqrt[6]{ a }\\---------------\)