Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{1}}{a^{\frac{-5}{3}}}\\= a^{ 1 - (\frac{-5}{3}) }= a^{\frac{8}{3}}\\=\sqrt[3]{ a^{8} }=a^{2}.\sqrt[3]{ a^{2} }\\---------------\)
2. \(\dfrac{x^{-1}}{x^{\frac{1}{5}}}\\= x^{ -1 - \frac{1}{5} }= x^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ x^{6} }}\\=\frac{1}{x.\sqrt[5]{ x }}=\frac{1}{x.\sqrt[5]{ x }} \color{purple}{\frac{\sqrt[5]{ x^{4} }}{\sqrt[5]{ x^{4} }}} \\=\frac{\sqrt[5]{ x^{4} }}{x^{2}}\\---------------\)
3. \(\dfrac{y^{\frac{1}{4}}}{y^{\frac{1}{3}}}\\= y^{ \frac{1}{4} - \frac{1}{3} }= y^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ y }}=\frac{1}{\sqrt[12]{ y }}. \color{purple}{\frac{\sqrt[12]{ y^{11} }}{\sqrt[12]{ y^{11} }}} \\=\frac{\sqrt[12]{ y^{11} }}{|y|}\\---------------\)
4. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{-2}{3} - (\frac{-2}{3}) }= q^{0}\\=1\\---------------\)
5. \(\dfrac{q^{\frac{3}{4}}}{q^{\frac{1}{2}}}\\= q^{ \frac{3}{4} - \frac{1}{2} }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
6. \(\dfrac{q^{2}}{q^{\frac{3}{2}}}\\= q^{ 2 - \frac{3}{2} }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
7. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{-5}{4}}}\\= a^{ \frac{2}{3} - (\frac{-5}{4}) }= a^{\frac{23}{12}}\\=\sqrt[12]{ a^{23} }=|a|.\sqrt[12]{ a^{11} }\\---------------\)
8. \(\dfrac{y^{\frac{-4}{3}}}{y^{-2}}\\= y^{ \frac{-4}{3} - (-2) }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
9. \(\dfrac{x^{\frac{-1}{6}}}{x^{\frac{2}{5}}}\\= x^{ \frac{-1}{6} - \frac{2}{5} }= x^{\frac{-17}{30}}\\=\frac{1}{\sqrt[30]{ x^{17} }}=\frac{1}{\sqrt[30]{ x^{17} }}. \color{purple}{\frac{\sqrt[30]{ x^{13} }}{\sqrt[30]{ x^{13} }}} \\=\frac{\sqrt[30]{ x^{13} }}{|x|}\\---------------\)
10. \(\dfrac{q^{-1}}{q^{-1}}\\= q^{ -1 - (-1) }= q^{0}\\=1\\---------------\)
11. \(\dfrac{x^{\frac{-1}{6}}}{x^{\frac{4}{3}}}\\= x^{ \frac{-1}{6} - \frac{4}{3} }= x^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ x^{3} } }\\=\frac{1}{|x|. \sqrt{ x } }=\frac{1}{|x|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{2}|}\\---------------\)
12. \(\dfrac{a^{\frac{-1}{4}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{-1}{4} - (\frac{-1}{3}) }= a^{\frac{1}{12}}\\=\sqrt[12]{ a }\\---------------\)