Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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