Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-3}{2}}}{a^{-1}}\\= a^{ \frac{-3}{2} - (-1) }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
2. \(\dfrac{q^{1}}{q^{\frac{3}{4}}}\\= q^{ 1 - \frac{3}{4} }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
3. \(\dfrac{y^{1}}{y^{\frac{-2}{3}}}\\= y^{ 1 - (\frac{-2}{3}) }= y^{\frac{5}{3}}\\=\sqrt[3]{ y^{5} }=y.\sqrt[3]{ y^{2} }\\---------------\)
4. \(\dfrac{x^{\frac{-5}{2}}}{x^{\frac{1}{5}}}\\= x^{ \frac{-5}{2} - \frac{1}{5} }= x^{\frac{-27}{10}}\\=\frac{1}{\sqrt[10]{ x^{27} }}\\=\frac{1}{|x^{2}|.\sqrt[10]{ x^{7} }}=\frac{1}{|x^{2}|.\sqrt[10]{ x^{7} }} \color{purple}{\frac{\sqrt[10]{ x^{3} }}{\sqrt[10]{ x^{3} }}} \\=\frac{\sqrt[10]{ x^{3} }}{|x^{3}|}\\---------------\)
5. \(\dfrac{a^{\frac{-4}{3}}}{a^{-2}}\\= a^{ \frac{-4}{3} - (-2) }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
6. \(\dfrac{a^{\frac{-2}{3}}}{a^{1}}\\= a^{ \frac{-2}{3} - 1 }= a^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ a^{5} }}\\=\frac{1}{a.\sqrt[3]{ a^{2} }}=\frac{1}{a.\sqrt[3]{ a^{2} }} \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{2}}\\---------------\)
7. \(\dfrac{a^{1}}{a^{\frac{-5}{6}}}\\= a^{ 1 - (\frac{-5}{6}) }= a^{\frac{11}{6}}\\=\sqrt[6]{ a^{11} }=|a|.\sqrt[6]{ a^{5} }\\---------------\)
8. \(\dfrac{q^{-2}}{q^{\frac{-5}{3}}}\\= q^{ -2 - (\frac{-5}{3}) }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
9. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{1}{4}}}\\= y^{ \frac{-1}{2} - \frac{1}{4} }= y^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ y^{3} }}=\frac{1}{\sqrt[4]{ y^{3} }}. \color{purple}{\frac{\sqrt[4]{ y }}{\sqrt[4]{ y }}} \\=\frac{\sqrt[4]{ y }}{|y|}\\---------------\)
10. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{-3}{2}}}\\= x^{ \frac{2}{3} - (\frac{-3}{2}) }= x^{\frac{13}{6}}\\=\sqrt[6]{ x^{13} }=|x^{2}|.\sqrt[6]{ x }\\---------------\)
11. \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{2}{3}}}\\= x^{ \frac{-2}{3} - \frac{2}{3} }= x^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ x^{4} }}\\=\frac{1}{x.\sqrt[3]{ x }}=\frac{1}{x.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{2}}\\---------------\)
12. \(\dfrac{x^{\frac{5}{4}}}{x^{\frac{-5}{6}}}\\= x^{ \frac{5}{4} - (\frac{-5}{6}) }= x^{\frac{25}{12}}\\=\sqrt[12]{ x^{25} }=|x^{2}|.\sqrt[12]{ x }\\---------------\)