Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{5}{6}}}{x^{\frac{-2}{3}}}\\= x^{ \frac{5}{6} - (\frac{-2}{3}) }= x^{\frac{3}{2}}\\= \sqrt{ x^{3} } =|x|. \sqrt{ x } \\---------------\)
2. \(\dfrac{q^{\frac{-2}{5}}}{q^{\frac{5}{2}}}\\= q^{ \frac{-2}{5} - \frac{5}{2} }= q^{\frac{-29}{10}}\\=\frac{1}{\sqrt[10]{ q^{29} }}\\=\frac{1}{|q^{2}|.\sqrt[10]{ q^{9} }}=\frac{1}{|q^{2}|.\sqrt[10]{ q^{9} }} \color{purple}{\frac{\sqrt[10]{ q }}{\sqrt[10]{ q }}} \\=\frac{\sqrt[10]{ q }}{|q^{3}|}\\---------------\)
3. \(\dfrac{a^{1}}{a^{\frac{-1}{2}}}\\= a^{ 1 - (\frac{-1}{2}) }= a^{\frac{3}{2}}\\= \sqrt{ a^{3} } =|a|. \sqrt{ a } \\---------------\)
4. \(\dfrac{x^{\frac{-5}{2}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{-5}{2} - (\frac{-1}{3}) }= x^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ x^{13} }}\\=\frac{1}{|x^{2}|.\sqrt[6]{ x }}=\frac{1}{|x^{2}|.\sqrt[6]{ x }} \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x^{3}|}\\---------------\)
5. \(\dfrac{x^{\frac{-5}{2}}}{x^{\frac{1}{2}}}\\= x^{ \frac{-5}{2} - \frac{1}{2} }= x^{-3}\\=\frac{1}{x^{3}}\\---------------\)
6. \(\dfrac{x^{\frac{1}{3}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{1}{3} - (\frac{-1}{2}) }= x^{\frac{5}{6}}\\=\sqrt[6]{ x^{5} }\\---------------\)
7. \(\dfrac{q^{-1}}{q^{-1}}\\= q^{ -1 - (-1) }= q^{0}\\=1\\---------------\)
8. \(\dfrac{y^{\frac{-5}{4}}}{y^{-1}}\\= y^{ \frac{-5}{4} - (-1) }= y^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ y }}=\frac{1}{\sqrt[4]{ y }}. \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y|}\\---------------\)
9. \(\dfrac{a^{\frac{-1}{4}}}{a^{\frac{5}{6}}}\\= a^{ \frac{-1}{4} - \frac{5}{6} }= a^{\frac{-13}{12}}\\=\frac{1}{\sqrt[12]{ a^{13} }}\\=\frac{1}{|a|.\sqrt[12]{ a }}=\frac{1}{|a|.\sqrt[12]{ a }} \color{purple}{\frac{\sqrt[12]{ a^{11} }}{\sqrt[12]{ a^{11} }}} \\=\frac{\sqrt[12]{ a^{11} }}{|a^{2}|}\\---------------\)
10. \(\dfrac{y^{\frac{-1}{4}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{-1}{4} - (\frac{-2}{3}) }= y^{\frac{5}{12}}\\=\sqrt[12]{ y^{5} }\\---------------\)
11. \(\dfrac{x^{\frac{3}{4}}}{x^{\frac{1}{5}}}\\= x^{ \frac{3}{4} - \frac{1}{5} }= x^{\frac{11}{20}}\\=\sqrt[20]{ x^{11} }\\---------------\)
12. \(\dfrac{y^{\frac{-2}{3}}}{y^{-2}}\\= y^{ \frac{-2}{3} - (-2) }= y^{\frac{4}{3}}\\=\sqrt[3]{ y^{4} }=y.\sqrt[3]{ y }\\---------------\)