Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-4}{3}}}{y^{\frac{4}{3}}}\\= y^{ \frac{-4}{3} - \frac{4}{3} }= y^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ y^{8} }}\\=\frac{1}{y^{2}.\sqrt[3]{ y^{2} }}=\frac{1}{y^{2}.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{3}}\\---------------\)
2. \(\dfrac{x^{\frac{3}{2}}}{x^{\frac{-5}{2}}}\\= x^{ \frac{3}{2} - (\frac{-5}{2}) }= x^{4}\\\\---------------\)
3. \(\dfrac{y^{\frac{1}{3}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{1}{3} - (\frac{-1}{2}) }= y^{\frac{5}{6}}\\=\sqrt[6]{ y^{5} }\\---------------\)
4. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{1}{3} - (\frac{-2}{3}) }= a^{1}\\\\---------------\)
5. \(\dfrac{q^{-1}}{q^{1}}\\= q^{ -1 - 1 }= q^{-2}\\=\frac{1}{q^{2}}\\---------------\)
6. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{2}{3}}}\\= y^{ \frac{-1}{3} - \frac{2}{3} }= y^{-1}\\=\frac{1}{y}\\---------------\)
7. \(\dfrac{y^{1}}{y^{\frac{5}{2}}}\\= y^{ 1 - \frac{5}{2} }= y^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ y^{3} } }\\=\frac{1}{|y|. \sqrt{ y } }=\frac{1}{|y|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{2}|}\\---------------\)
8. \(\dfrac{a^{\frac{3}{5}}}{a^{\frac{-1}{6}}}\\= a^{ \frac{3}{5} - (\frac{-1}{6}) }= a^{\frac{23}{30}}\\=\sqrt[30]{ a^{23} }\\---------------\)
9. \(\dfrac{q^{\frac{-3}{4}}}{q^{1}}\\= q^{ \frac{-3}{4} - 1 }= q^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ q^{7} }}\\=\frac{1}{|q|.\sqrt[4]{ q^{3} }}=\frac{1}{|q|.\sqrt[4]{ q^{3} }} \color{purple}{\frac{\sqrt[4]{ q }}{\sqrt[4]{ q }}} \\=\frac{\sqrt[4]{ q }}{|q^{2}|}\\---------------\)
10. \(\dfrac{y^{\frac{-1}{2}}}{y^{2}}\\= y^{ \frac{-1}{2} - 2 }= y^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ y^{5} } }\\=\frac{1}{|y^{2}|. \sqrt{ y } }=\frac{1}{|y^{2}|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{3}|}\\---------------\)
11. \(\dfrac{y^{-2}}{y^{\frac{-1}{3}}}\\= y^{ -2 - (\frac{-1}{3}) }= y^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ y^{5} }}\\=\frac{1}{y.\sqrt[3]{ y^{2} }}=\frac{1}{y.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{2}}\\---------------\)
12. \(\dfrac{a^{\frac{1}{6}}}{a^{-2}}\\= a^{ \frac{1}{6} - (-2) }= a^{\frac{13}{6}}\\=\sqrt[6]{ a^{13} }=|a^{2}|.\sqrt[6]{ a }\\---------------\)