Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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