Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{3}{2}}}\\= y^{ \frac{2}{3} - \frac{3}{2} }= y^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ y^{5} }}=\frac{1}{\sqrt[6]{ y^{5} }}. \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y|}\\---------------\)
2. \(\dfrac{a^{\frac{-5}{3}}}{a^{\frac{1}{5}}}\\= a^{ \frac{-5}{3} - \frac{1}{5} }= a^{\frac{-28}{15}}\\=\frac{1}{\sqrt[15]{ a^{28} }}\\=\frac{1}{a.\sqrt[15]{ a^{13} }}=\frac{1}{a.\sqrt[15]{ a^{13} }} \color{purple}{\frac{\sqrt[15]{ a^{2} }}{\sqrt[15]{ a^{2} }}} \\=\frac{\sqrt[15]{ a^{2} }}{a^{2}}\\---------------\)
3. \(\dfrac{x^{2}}{x^{-2}}\\= x^{ 2 - (-2) }= x^{4}\\\\---------------\)
4. \(\dfrac{q^{\frac{-5}{2}}}{q^{\frac{-1}{6}}}\\= q^{ \frac{-5}{2} - (\frac{-1}{6}) }= q^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ q^{7} }}\\=\frac{1}{q^{2}.\sqrt[3]{ q }}=\frac{1}{q^{2}.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{3}}\\---------------\)
5. \(\dfrac{x^{\frac{5}{3}}}{x^{\frac{5}{3}}}\\= x^{ \frac{5}{3} - \frac{5}{3} }= x^{0}\\=1\\---------------\)
6. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{1}{2} - (\frac{-1}{3}) }= x^{\frac{5}{6}}\\=\sqrt[6]{ x^{5} }\\---------------\)
7. \(\dfrac{y^{-1}}{y^{-1}}\\= y^{ -1 - (-1) }= y^{0}\\=1\\---------------\)
8. \(\dfrac{y^{\frac{-3}{4}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{-3}{4} - (\frac{-1}{3}) }= y^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ y^{5} }}=\frac{1}{\sqrt[12]{ y^{5} }}. \color{purple}{\frac{\sqrt[12]{ y^{7} }}{\sqrt[12]{ y^{7} }}} \\=\frac{\sqrt[12]{ y^{7} }}{|y|}\\---------------\)
9. \(\dfrac{x^{1}}{x^{\frac{-1}{4}}}\\= x^{ 1 - (\frac{-1}{4}) }= x^{\frac{5}{4}}\\=\sqrt[4]{ x^{5} }=|x|.\sqrt[4]{ x }\\---------------\)
10. \(\dfrac{x^{-1}}{x^{\frac{-3}{2}}}\\= x^{ -1 - (\frac{-3}{2}) }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
11. \(\dfrac{x^{\frac{-2}{5}}}{x^{\frac{-3}{2}}}\\= x^{ \frac{-2}{5} - (\frac{-3}{2}) }= x^{\frac{11}{10}}\\=\sqrt[10]{ x^{11} }=|x|.\sqrt[10]{ x }\\---------------\)
12. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{-3}{5}}}\\= x^{ \frac{1}{2} - (\frac{-3}{5}) }= x^{\frac{11}{10}}\\=\sqrt[10]{ x^{11} }=|x|.\sqrt[10]{ x }\\---------------\)