Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{-4}{5}}}\\= x^{ \frac{2}{3} - (\frac{-4}{5}) }= x^{\frac{22}{15}}\\=\sqrt[15]{ x^{22} }=x.\sqrt[15]{ x^{7} }\\---------------\)
2. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{-5}{2}}}\\= q^{ \frac{-1}{2} - (\frac{-5}{2}) }= q^{2}\\\\---------------\)
3. \(\dfrac{q^{\frac{3}{2}}}{q^{-1}}\\= q^{ \frac{3}{2} - (-1) }= q^{\frac{5}{2}}\\= \sqrt{ q^{5} } =|q^{2}|. \sqrt{ q } \\---------------\)
4. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{-1}{2} - (\frac{-1}{2}) }= y^{0}\\=1\\---------------\)
5. \(\dfrac{y^{1}}{y^{\frac{-4}{5}}}\\= y^{ 1 - (\frac{-4}{5}) }= y^{\frac{9}{5}}\\=\sqrt[5]{ y^{9} }=y.\sqrt[5]{ y^{4} }\\---------------\)
6. \(\dfrac{y^{\frac{4}{5}}}{y^{\frac{-5}{4}}}\\= y^{ \frac{4}{5} - (\frac{-5}{4}) }= y^{\frac{41}{20}}\\=\sqrt[20]{ y^{41} }=|y^{2}|.\sqrt[20]{ y }\\---------------\)
7. \(\dfrac{a^{\frac{2}{3}}}{a^{1}}\\= a^{ \frac{2}{3} - 1 }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
8. \(\dfrac{q^{\frac{-1}{6}}}{q^{\frac{-3}{2}}}\\= q^{ \frac{-1}{6} - (\frac{-3}{2}) }= q^{\frac{4}{3}}\\=\sqrt[3]{ q^{4} }=q.\sqrt[3]{ q }\\---------------\)
9. \(\dfrac{q^{-1}}{q^{\frac{-1}{2}}}\\= q^{ -1 - (\frac{-1}{2}) }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
10. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{4}{5}}}\\= y^{ \frac{-1}{2} - \frac{4}{5} }= y^{\frac{-13}{10}}\\=\frac{1}{\sqrt[10]{ y^{13} }}\\=\frac{1}{|y|.\sqrt[10]{ y^{3} }}=\frac{1}{|y|.\sqrt[10]{ y^{3} }} \color{purple}{\frac{\sqrt[10]{ y^{7} }}{\sqrt[10]{ y^{7} }}} \\=\frac{\sqrt[10]{ y^{7} }}{|y^{2}|}\\---------------\)
11. \(\dfrac{x^{\frac{1}{3}}}{x^{\frac{1}{3}}}\\= x^{ \frac{1}{3} - \frac{1}{3} }= x^{0}\\=1\\---------------\)
12. \(\dfrac{q^{\frac{4}{3}}}{q^{\frac{-4}{5}}}\\= q^{ \frac{4}{3} - (\frac{-4}{5}) }= q^{\frac{32}{15}}\\=\sqrt[15]{ q^{32} }=q^{2}.\sqrt[15]{ q^{2} }\\---------------\)