Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{1}{2}}}{x^{1}}\\= x^{ \frac{1}{2} - 1 }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
2. \(\dfrac{y^{2}}{y^{\frac{-5}{4}}}\\= y^{ 2 - (\frac{-5}{4}) }= y^{\frac{13}{4}}\\=\sqrt[4]{ y^{13} }=|y^{3}|.\sqrt[4]{ y }\\---------------\)
3. \(\dfrac{a^{\frac{5}{3}}}{a^{1}}\\= a^{ \frac{5}{3} - 1 }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
4. \(\dfrac{a^{\frac{-1}{6}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{-1}{6} - (\frac{-1}{3}) }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)
5. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{-5}{2}}}\\= a^{ \frac{2}{3} - (\frac{-5}{2}) }= a^{\frac{19}{6}}\\=\sqrt[6]{ a^{19} }=|a^{3}|.\sqrt[6]{ a }\\---------------\)
6. \(\dfrac{y^{\frac{5}{2}}}{y^{-1}}\\= y^{ \frac{5}{2} - (-1) }= y^{\frac{7}{2}}\\= \sqrt{ y^{7} } =|y^{3}|. \sqrt{ y } \\---------------\)
7. \(\dfrac{y^{\frac{2}{3}}}{y^{-1}}\\= y^{ \frac{2}{3} - (-1) }= y^{\frac{5}{3}}\\=\sqrt[3]{ y^{5} }=y.\sqrt[3]{ y^{2} }\\---------------\)
8. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{5}{3}}}\\= a^{ \frac{-1}{3} - \frac{5}{3} }= a^{-2}\\=\frac{1}{a^{2}}\\---------------\)
9. \(\dfrac{q^{\frac{-5}{2}}}{q^{\frac{-3}{2}}}\\= q^{ \frac{-5}{2} - (\frac{-3}{2}) }= q^{-1}\\=\frac{1}{q}\\---------------\)
10. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{4}{3}}}\\= a^{ \frac{2}{3} - \frac{4}{3} }= a^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ a^{2} }}=\frac{1}{\sqrt[3]{ a^{2} }}. \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a}\\---------------\)
11. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{-5}{4}}}\\= a^{ \frac{-1}{2} - (\frac{-5}{4}) }= a^{\frac{3}{4}}\\=\sqrt[4]{ a^{3} }\\---------------\)
12. \(\dfrac{a^{-1}}{a^{\frac{1}{5}}}\\= a^{ -1 - \frac{1}{5} }= a^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ a^{6} }}\\=\frac{1}{a.\sqrt[5]{ a }}=\frac{1}{a.\sqrt[5]{ a }} \color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a^{2}}\\---------------\)