Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{-2}}{a^{\frac{2}{3}}}\\= a^{ -2 - \frac{2}{3} }= a^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ a^{8} }}\\=\frac{1}{a^{2}.\sqrt[3]{ a^{2} }}=\frac{1}{a^{2}.\sqrt[3]{ a^{2} }} \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{3}}\\---------------\)
2. \(\dfrac{a^{1}}{a^{\frac{3}{2}}}\\= a^{ 1 - \frac{3}{2} }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
3. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{-3}{4}}}\\= q^{ \frac{1}{2} - (\frac{-3}{4}) }= q^{\frac{5}{4}}\\=\sqrt[4]{ q^{5} }=|q|.\sqrt[4]{ q }\\---------------\)
4. \(\dfrac{y^{\frac{1}{2}}}{y^{1}}\\= y^{ \frac{1}{2} - 1 }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
5. \(\dfrac{y^{\frac{-5}{2}}}{y^{\frac{1}{6}}}\\= y^{ \frac{-5}{2} - \frac{1}{6} }= y^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ y^{8} }}\\=\frac{1}{y^{2}.\sqrt[3]{ y^{2} }}=\frac{1}{y^{2}.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{3}}\\---------------\)
6. \(\dfrac{x^{\frac{-1}{2}}}{x^{-2}}\\= x^{ \frac{-1}{2} - (-2) }= x^{\frac{3}{2}}\\= \sqrt{ x^{3} } =|x|. \sqrt{ x } \\---------------\)
7. \(\dfrac{a^{1}}{a^{\frac{1}{3}}}\\= a^{ 1 - \frac{1}{3} }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
8. \(\dfrac{x^{\frac{2}{3}}}{x^{1}}\\= x^{ \frac{2}{3} - 1 }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
9. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{-4}{5}}}\\= a^{ \frac{-1}{2} - (\frac{-4}{5}) }= a^{\frac{3}{10}}\\=\sqrt[10]{ a^{3} }\\---------------\)
10. \(\dfrac{q^{\frac{-1}{4}}}{q^{\frac{-3}{5}}}\\= q^{ \frac{-1}{4} - (\frac{-3}{5}) }= q^{\frac{7}{20}}\\=\sqrt[20]{ q^{7} }\\---------------\)
11. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{-1}{5}}}\\= q^{ \frac{2}{3} - (\frac{-1}{5}) }= q^{\frac{13}{15}}\\=\sqrt[15]{ q^{13} }\\---------------\)
12. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{1}{2}}}\\= a^{ \frac{2}{3} - \frac{1}{2} }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)