Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-1}{2}}}{q^{-2}}\\= q^{ \frac{-1}{2} - (-2) }= q^{\frac{3}{2}}\\= \sqrt{ q^{3} } =|q|. \sqrt{ q } \\---------------\)
2. \(\dfrac{q^{-1}}{q^{\frac{1}{2}}}\\= q^{ -1 - \frac{1}{2} }= q^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ q^{3} } }\\=\frac{1}{|q|. \sqrt{ q } }=\frac{1}{|q|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{2}|}\\---------------\)
3. \(\dfrac{q^{\frac{3}{4}}}{q^{\frac{1}{2}}}\\= q^{ \frac{3}{4} - \frac{1}{2} }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
4. \(\dfrac{x^{\frac{1}{2}}}{x^{2}}\\= x^{ \frac{1}{2} - 2 }= x^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ x^{3} } }\\=\frac{1}{|x|. \sqrt{ x } }=\frac{1}{|x|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{2}|}\\---------------\)
5. \(\dfrac{y^{\frac{-4}{5}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{-4}{5} - (\frac{-1}{3}) }= y^{\frac{-7}{15}}\\=\frac{1}{\sqrt[15]{ y^{7} }}=\frac{1}{\sqrt[15]{ y^{7} }}. \color{purple}{\frac{\sqrt[15]{ y^{8} }}{\sqrt[15]{ y^{8} }}} \\=\frac{\sqrt[15]{ y^{8} }}{y}\\---------------\)
6. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{1}{3}}}\\= a^{ \frac{1}{3} - \frac{1}{3} }= a^{0}\\=1\\---------------\)
7. \(\dfrac{x^{\frac{1}{3}}}{x^{\frac{4}{5}}}\\= x^{ \frac{1}{3} - \frac{4}{5} }= x^{\frac{-7}{15}}\\=\frac{1}{\sqrt[15]{ x^{7} }}=\frac{1}{\sqrt[15]{ x^{7} }}. \color{purple}{\frac{\sqrt[15]{ x^{8} }}{\sqrt[15]{ x^{8} }}} \\=\frac{\sqrt[15]{ x^{8} }}{x}\\---------------\)
8. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{5}{4}}}\\= a^{ \frac{1}{3} - \frac{5}{4} }= a^{\frac{-11}{12}}\\=\frac{1}{\sqrt[12]{ a^{11} }}=\frac{1}{\sqrt[12]{ a^{11} }}. \color{purple}{\frac{\sqrt[12]{ a }}{\sqrt[12]{ a }}} \\=\frac{\sqrt[12]{ a }}{|a|}\\---------------\)
9. \(\dfrac{y^{\frac{-2}{5}}}{y^{1}}\\= y^{ \frac{-2}{5} - 1 }= y^{\frac{-7}{5}}\\=\frac{1}{\sqrt[5]{ y^{7} }}\\=\frac{1}{y.\sqrt[5]{ y^{2} }}=\frac{1}{y.\sqrt[5]{ y^{2} }} \color{purple}{\frac{\sqrt[5]{ y^{3} }}{\sqrt[5]{ y^{3} }}} \\=\frac{\sqrt[5]{ y^{3} }}{y^{2}}\\---------------\)
10. \(\dfrac{a^{\frac{-5}{2}}}{a^{-1}}\\= a^{ \frac{-5}{2} - (-1) }= a^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ a^{3} } }\\=\frac{1}{|a|. \sqrt{ a } }=\frac{1}{|a|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{2}|}\\---------------\)
11. \(\dfrac{a^{\frac{5}{4}}}{a^{-1}}\\= a^{ \frac{5}{4} - (-1) }= a^{\frac{9}{4}}\\=\sqrt[4]{ a^{9} }=|a^{2}|.\sqrt[4]{ a }\\---------------\)
12. \(\dfrac{q^{\frac{-3}{2}}}{q^{\frac{-5}{3}}}\\= q^{ \frac{-3}{2} - (\frac{-5}{3}) }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)