Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{-1}}{y^{-1}}\\= y^{ -1 - (-1) }= y^{0}\\=1\\---------------\)
2. \(\dfrac{a^{\frac{1}{5}}}{a^{-1}}\\= a^{ \frac{1}{5} - (-1) }= a^{\frac{6}{5}}\\=\sqrt[5]{ a^{6} }=a.\sqrt[5]{ a }\\---------------\)
3. \(\dfrac{a^{\frac{1}{5}}}{a^{\frac{4}{5}}}\\= a^{ \frac{1}{5} - \frac{4}{5} }= a^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ a^{3} }}=\frac{1}{\sqrt[5]{ a^{3} }}. \color{purple}{\frac{\sqrt[5]{ a^{2} }}{\sqrt[5]{ a^{2} }}} \\=\frac{\sqrt[5]{ a^{2} }}{a}\\---------------\)
4. \(\dfrac{x^{\frac{1}{6}}}{x^{-1}}\\= x^{ \frac{1}{6} - (-1) }= x^{\frac{7}{6}}\\=\sqrt[6]{ x^{7} }=|x|.\sqrt[6]{ x }\\---------------\)
5. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{-4}{5}}}\\= x^{ \frac{-1}{3} - (\frac{-4}{5}) }= x^{\frac{7}{15}}\\=\sqrt[15]{ x^{7} }\\---------------\)
6. \(\dfrac{a^{\frac{2}{5}}}{a^{\frac{-5}{3}}}\\= a^{ \frac{2}{5} - (\frac{-5}{3}) }= a^{\frac{31}{15}}\\=\sqrt[15]{ a^{31} }=a^{2}.\sqrt[15]{ a }\\---------------\)
7. \(\dfrac{y^{\frac{1}{6}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{1}{6} - (\frac{-1}{3}) }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
8. \(\dfrac{a^{\frac{-2}{5}}}{a^{\frac{2}{3}}}\\= a^{ \frac{-2}{5} - \frac{2}{3} }= a^{\frac{-16}{15}}\\=\frac{1}{\sqrt[15]{ a^{16} }}\\=\frac{1}{a.\sqrt[15]{ a }}=\frac{1}{a.\sqrt[15]{ a }} \color{purple}{\frac{\sqrt[15]{ a^{14} }}{\sqrt[15]{ a^{14} }}} \\=\frac{\sqrt[15]{ a^{14} }}{a^{2}}\\---------------\)
9. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{1}{5}}}\\= y^{ \frac{1}{2} - \frac{1}{5} }= y^{\frac{3}{10}}\\=\sqrt[10]{ y^{3} }\\---------------\)
10. \(\dfrac{x^{\frac{-5}{3}}}{x^{\frac{1}{3}}}\\= x^{ \frac{-5}{3} - \frac{1}{3} }= x^{-2}\\=\frac{1}{x^{2}}\\---------------\)
11. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{1}{3}}}\\= q^{ \frac{1}{2} - \frac{1}{3} }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
12. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{-2}{3} - (\frac{-1}{3}) }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)