Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{-5}{6}}}\\= x^{ \frac{-2}{3} - (\frac{-5}{6}) }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
2. \(\dfrac{y^{\frac{-1}{5}}}{y^{\frac{5}{2}}}\\= y^{ \frac{-1}{5} - \frac{5}{2} }= y^{\frac{-27}{10}}\\=\frac{1}{\sqrt[10]{ y^{27} }}\\=\frac{1}{|y^{2}|.\sqrt[10]{ y^{7} }}=\frac{1}{|y^{2}|.\sqrt[10]{ y^{7} }} \color{purple}{\frac{\sqrt[10]{ y^{3} }}{\sqrt[10]{ y^{3} }}} \\=\frac{\sqrt[10]{ y^{3} }}{|y^{3}|}\\---------------\)
3. \(\dfrac{x^{\frac{-5}{3}}}{x^{\frac{-4}{5}}}\\= x^{ \frac{-5}{3} - (\frac{-4}{5}) }= x^{\frac{-13}{15}}\\=\frac{1}{\sqrt[15]{ x^{13} }}=\frac{1}{\sqrt[15]{ x^{13} }}. \color{purple}{\frac{\sqrt[15]{ x^{2} }}{\sqrt[15]{ x^{2} }}} \\=\frac{\sqrt[15]{ x^{2} }}{x}\\---------------\)
4. \(\dfrac{q^{\frac{1}{5}}}{q^{\frac{-4}{5}}}\\= q^{ \frac{1}{5} - (\frac{-4}{5}) }= q^{1}\\\\---------------\)
5. \(\dfrac{x^{\frac{2}{3}}}{x^{-1}}\\= x^{ \frac{2}{3} - (-1) }= x^{\frac{5}{3}}\\=\sqrt[3]{ x^{5} }=x.\sqrt[3]{ x^{2} }\\---------------\)
6. \(\dfrac{q^{\frac{-4}{5}}}{q^{\frac{2}{3}}}\\= q^{ \frac{-4}{5} - \frac{2}{3} }= q^{\frac{-22}{15}}\\=\frac{1}{\sqrt[15]{ q^{22} }}\\=\frac{1}{q.\sqrt[15]{ q^{7} }}=\frac{1}{q.\sqrt[15]{ q^{7} }} \color{purple}{\frac{\sqrt[15]{ q^{8} }}{\sqrt[15]{ q^{8} }}} \\=\frac{\sqrt[15]{ q^{8} }}{q^{2}}\\---------------\)
7. \(\dfrac{q^{-1}}{q^{\frac{-1}{6}}}\\= q^{ -1 - (\frac{-1}{6}) }= q^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ q^{5} }}=\frac{1}{\sqrt[6]{ q^{5} }}. \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q|}\\---------------\)
8. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{-1}{5}}}\\= q^{ \frac{1}{2} - (\frac{-1}{5}) }= q^{\frac{7}{10}}\\=\sqrt[10]{ q^{7} }\\---------------\)
9. \(\dfrac{x^{\frac{-1}{2}}}{x^{-2}}\\= x^{ \frac{-1}{2} - (-2) }= x^{\frac{3}{2}}\\= \sqrt{ x^{3} } =|x|. \sqrt{ x } \\---------------\)
10. \(\dfrac{q^{1}}{q^{\frac{-1}{3}}}\\= q^{ 1 - (\frac{-1}{3}) }= q^{\frac{4}{3}}\\=\sqrt[3]{ q^{4} }=q.\sqrt[3]{ q }\\---------------\)
11. \(\dfrac{a^{\frac{2}{5}}}{a^{\frac{-5}{4}}}\\= a^{ \frac{2}{5} - (\frac{-5}{4}) }= a^{\frac{33}{20}}\\=\sqrt[20]{ a^{33} }=|a|.\sqrt[20]{ a^{13} }\\---------------\)
12. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{2}{3}}}\\= y^{ \frac{-2}{3} - \frac{2}{3} }= y^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ y^{4} }}\\=\frac{1}{y.\sqrt[3]{ y }}=\frac{1}{y.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{2}}\\---------------\)