Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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