Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-2}{5}}}{y^{\frac{2}{3}}}\\= y^{ \frac{-2}{5} - \frac{2}{3} }= y^{\frac{-16}{15}}\\=\frac{1}{\sqrt[15]{ y^{16} }}\\=\frac{1}{y.\sqrt[15]{ y }}=\frac{1}{y.\sqrt[15]{ y }} \color{purple}{\frac{\sqrt[15]{ y^{14} }}{\sqrt[15]{ y^{14} }}} \\=\frac{\sqrt[15]{ y^{14} }}{y^{2}}\\---------------\)
2. \(\dfrac{y^{\frac{3}{4}}}{y^{-2}}\\= y^{ \frac{3}{4} - (-2) }= y^{\frac{11}{4}}\\=\sqrt[4]{ y^{11} }=|y^{2}|.\sqrt[4]{ y^{3} }\\---------------\)
3. \(\dfrac{a^{-1}}{a^{\frac{-4}{5}}}\\= a^{ -1 - (\frac{-4}{5}) }= a^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ a }}=\frac{1}{\sqrt[5]{ a }}. \color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a}\\---------------\)
4. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{2}{3}}}\\= q^{ \frac{2}{3} - \frac{2}{3} }= q^{0}\\=1\\---------------\)
5. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{-2}{5}}}\\= a^{ \frac{-2}{3} - (\frac{-2}{5}) }= a^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ a^{4} }}=\frac{1}{\sqrt[15]{ a^{4} }}. \color{purple}{\frac{\sqrt[15]{ a^{11} }}{\sqrt[15]{ a^{11} }}} \\=\frac{\sqrt[15]{ a^{11} }}{a}\\---------------\)
6. \(\dfrac{y^{\frac{-1}{5}}}{y^{\frac{3}{4}}}\\= y^{ \frac{-1}{5} - \frac{3}{4} }= y^{\frac{-19}{20}}\\=\frac{1}{\sqrt[20]{ y^{19} }}=\frac{1}{\sqrt[20]{ y^{19} }}. \color{purple}{\frac{\sqrt[20]{ y }}{\sqrt[20]{ y }}} \\=\frac{\sqrt[20]{ y }}{|y|}\\---------------\)
7. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{2}{3} - (\frac{-1}{2}) }= x^{\frac{7}{6}}\\=\sqrt[6]{ x^{7} }=|x|.\sqrt[6]{ x }\\---------------\)
8. \(\dfrac{a^{\frac{-2}{3}}}{a^{1}}\\= a^{ \frac{-2}{3} - 1 }= a^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ a^{5} }}\\=\frac{1}{a.\sqrt[3]{ a^{2} }}=\frac{1}{a.\sqrt[3]{ a^{2} }} \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{2}}\\---------------\)
9. \(\dfrac{x^{\frac{-5}{6}}}{x^{\frac{-5}{2}}}\\= x^{ \frac{-5}{6} - (\frac{-5}{2}) }= x^{\frac{5}{3}}\\=\sqrt[3]{ x^{5} }=x.\sqrt[3]{ x^{2} }\\---------------\)
10. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{1}{2} - (\frac{-1}{3}) }= x^{\frac{5}{6}}\\=\sqrt[6]{ x^{5} }\\---------------\)
11. \(\dfrac{a^{\frac{5}{6}}}{a^{\frac{1}{2}}}\\= a^{ \frac{5}{6} - \frac{1}{2} }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
12. \(\dfrac{a^{\frac{-4}{3}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{-4}{3} - (\frac{-1}{2}) }= a^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ a^{5} }}=\frac{1}{\sqrt[6]{ a^{5} }}. \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a|}\\---------------\)