Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-4}{3}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{-4}{3} - (\frac{-1}{2}) }= a^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ a^{5} }}=\frac{1}{\sqrt[6]{ a^{5} }}. \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a|}\\---------------\)
2. \(\dfrac{q^{2}}{q^{\frac{-1}{2}}}\\= q^{ 2 - (\frac{-1}{2}) }= q^{\frac{5}{2}}\\= \sqrt{ q^{5} } =|q^{2}|. \sqrt{ q } \\---------------\)
3. \(\dfrac{q^{\frac{3}{4}}}{q^{\frac{-2}{5}}}\\= q^{ \frac{3}{4} - (\frac{-2}{5}) }= q^{\frac{23}{20}}\\=\sqrt[20]{ q^{23} }=|q|.\sqrt[20]{ q^{3} }\\---------------\)
4. \(\dfrac{y^{\frac{1}{4}}}{y^{2}}\\= y^{ \frac{1}{4} - 2 }= y^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[4]{ y^{3} }}=\frac{1}{|y|.\sqrt[4]{ y^{3} }} \color{purple}{\frac{\sqrt[4]{ y }}{\sqrt[4]{ y }}} \\=\frac{\sqrt[4]{ y }}{|y^{2}|}\\---------------\)
5. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{1}{3}}}\\= q^{ \frac{-1}{2} - \frac{1}{3} }= q^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ q^{5} }}=\frac{1}{\sqrt[6]{ q^{5} }}. \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q|}\\---------------\)
6. \(\dfrac{y^{2}}{y^{\frac{-1}{3}}}\\= y^{ 2 - (\frac{-1}{3}) }= y^{\frac{7}{3}}\\=\sqrt[3]{ y^{7} }=y^{2}.\sqrt[3]{ y }\\---------------\)
7. \(\dfrac{q^{1}}{q^{\frac{-1}{3}}}\\= q^{ 1 - (\frac{-1}{3}) }= q^{\frac{4}{3}}\\=\sqrt[3]{ q^{4} }=q.\sqrt[3]{ q }\\---------------\)
8. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{-3}{2}}}\\= x^{ \frac{-1}{3} - (\frac{-3}{2}) }= x^{\frac{7}{6}}\\=\sqrt[6]{ x^{7} }=|x|.\sqrt[6]{ x }\\---------------\)
9. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{-4}{5}}}\\= a^{ \frac{-2}{3} - (\frac{-4}{5}) }= a^{\frac{2}{15}}\\=\sqrt[15]{ a^{2} }\\---------------\)
10. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{-1}{6}}}\\= x^{ \frac{1}{2} - (\frac{-1}{6}) }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
11. \(\dfrac{q^{1}}{q^{\frac{-1}{5}}}\\= q^{ 1 - (\frac{-1}{5}) }= q^{\frac{6}{5}}\\=\sqrt[5]{ q^{6} }=q.\sqrt[5]{ q }\\---------------\)
12. \(\dfrac{x^{\frac{-1}{5}}}{x^{\frac{5}{4}}}\\= x^{ \frac{-1}{5} - \frac{5}{4} }= x^{\frac{-29}{20}}\\=\frac{1}{\sqrt[20]{ x^{29} }}\\=\frac{1}{|x|.\sqrt[20]{ x^{9} }}=\frac{1}{|x|.\sqrt[20]{ x^{9} }} \color{purple}{\frac{\sqrt[20]{ x^{11} }}{\sqrt[20]{ x^{11} }}} \\=\frac{\sqrt[20]{ x^{11} }}{|x^{2}|}\\---------------\)