Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{-2}}{a^{\frac{-5}{3}}}\\= a^{ -2 - (\frac{-5}{3}) }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
2. \(\dfrac{a^{\frac{-2}{5}}}{a^{\frac{-4}{5}}}\\= a^{ \frac{-2}{5} - (\frac{-4}{5}) }= a^{\frac{2}{5}}\\=\sqrt[5]{ a^{2} }\\---------------\)
3. \(\dfrac{a^{-1}}{a^{\frac{5}{3}}}\\= a^{ -1 - \frac{5}{3} }= a^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ a^{8} }}\\=\frac{1}{a^{2}.\sqrt[3]{ a^{2} }}=\frac{1}{a^{2}.\sqrt[3]{ a^{2} }} \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{3}}\\---------------\)
4. \(\dfrac{y^{-2}}{y^{\frac{1}{2}}}\\= y^{ -2 - \frac{1}{2} }= y^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ y^{5} } }\\=\frac{1}{|y^{2}|. \sqrt{ y } }=\frac{1}{|y^{2}|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{3}|}\\---------------\)
5. \(\dfrac{y^{\frac{3}{5}}}{y^{\frac{5}{2}}}\\= y^{ \frac{3}{5} - \frac{5}{2} }= y^{\frac{-19}{10}}\\=\frac{1}{\sqrt[10]{ y^{19} }}\\=\frac{1}{|y|.\sqrt[10]{ y^{9} }}=\frac{1}{|y|.\sqrt[10]{ y^{9} }} \color{purple}{\frac{\sqrt[10]{ y }}{\sqrt[10]{ y }}} \\=\frac{\sqrt[10]{ y }}{|y^{2}|}\\---------------\)
6. \(\dfrac{x^{-1}}{x^{-1}}\\= x^{ -1 - (-1) }= x^{0}\\=1\\---------------\)
7. \(\dfrac{a^{\frac{3}{5}}}{a^{1}}\\= a^{ \frac{3}{5} - 1 }= a^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ a^{2} }}=\frac{1}{\sqrt[5]{ a^{2} }}. \color{purple}{\frac{\sqrt[5]{ a^{3} }}{\sqrt[5]{ a^{3} }}} \\=\frac{\sqrt[5]{ a^{3} }}{a}\\---------------\)
8. \(\dfrac{x^{\frac{-5}{4}}}{x^{-1}}\\= x^{ \frac{-5}{4} - (-1) }= x^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ x }}=\frac{1}{\sqrt[4]{ x }}. \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x|}\\---------------\)
9. \(\dfrac{q^{\frac{2}{5}}}{q^{1}}\\= q^{ \frac{2}{5} - 1 }= q^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ q^{3} }}=\frac{1}{\sqrt[5]{ q^{3} }}. \color{purple}{\frac{\sqrt[5]{ q^{2} }}{\sqrt[5]{ q^{2} }}} \\=\frac{\sqrt[5]{ q^{2} }}{q}\\---------------\)
10. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{-5}{2}}}\\= q^{ \frac{-2}{3} - (\frac{-5}{2}) }= q^{\frac{11}{6}}\\=\sqrt[6]{ q^{11} }=|q|.\sqrt[6]{ q^{5} }\\---------------\)
11. \(\dfrac{x^{\frac{-5}{4}}}{x^{\frac{-2}{3}}}\\= x^{ \frac{-5}{4} - (\frac{-2}{3}) }= x^{\frac{-7}{12}}\\=\frac{1}{\sqrt[12]{ x^{7} }}=\frac{1}{\sqrt[12]{ x^{7} }}. \color{purple}{\frac{\sqrt[12]{ x^{5} }}{\sqrt[12]{ x^{5} }}} \\=\frac{\sqrt[12]{ x^{5} }}{|x|}\\---------------\)
12. \(\dfrac{y^{\frac{1}{6}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{1}{6} - (\frac{-1}{3}) }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)