Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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