Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{1}{2}}}{q^{1}}\\= q^{ \frac{1}{2} - 1 }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
2. \(\dfrac{x^{-1}}{x^{\frac{-5}{2}}}\\= x^{ -1 - (\frac{-5}{2}) }= x^{\frac{3}{2}}\\= \sqrt{ x^{3} } =|x|. \sqrt{ x } \\---------------\)
3. \(\dfrac{y^{-1}}{y^{\frac{1}{2}}}\\= y^{ -1 - \frac{1}{2} }= y^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ y^{3} } }\\=\frac{1}{|y|. \sqrt{ y } }=\frac{1}{|y|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{2}|}\\---------------\)
4. \(\dfrac{x^{\frac{-1}{3}}}{x^{-2}}\\= x^{ \frac{-1}{3} - (-2) }= x^{\frac{5}{3}}\\=\sqrt[3]{ x^{5} }=x.\sqrt[3]{ x^{2} }\\---------------\)
5. \(\dfrac{q^{-1}}{q^{-1}}\\= q^{ -1 - (-1) }= q^{0}\\=1\\---------------\)
6. \(\dfrac{a^{\frac{4}{3}}}{a^{\frac{4}{5}}}\\= a^{ \frac{4}{3} - \frac{4}{5} }= a^{\frac{8}{15}}\\=\sqrt[15]{ a^{8} }\\---------------\)
7. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{-1}{6}}}\\= a^{ \frac{-1}{3} - (\frac{-1}{6}) }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
8. \(\dfrac{q^{\frac{3}{4}}}{q^{\frac{-3}{4}}}\\= q^{ \frac{3}{4} - (\frac{-3}{4}) }= q^{\frac{3}{2}}\\= \sqrt{ q^{3} } =|q|. \sqrt{ q } \\---------------\)
9. \(\dfrac{y^{2}}{y^{-1}}\\= y^{ 2 - (-1) }= y^{3}\\\\---------------\)
10. \(\dfrac{q^{\frac{3}{4}}}{q^{\frac{-3}{5}}}\\= q^{ \frac{3}{4} - (\frac{-3}{5}) }= q^{\frac{27}{20}}\\=\sqrt[20]{ q^{27} }=|q|.\sqrt[20]{ q^{7} }\\---------------\)
11. \(\dfrac{x^{\frac{-5}{2}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{-5}{2} - (\frac{-1}{2}) }= x^{-2}\\=\frac{1}{x^{2}}\\---------------\)
12. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{-1}{5}}}\\= y^{ \frac{-1}{3} - (\frac{-1}{5}) }= y^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ y^{2} }}=\frac{1}{\sqrt[15]{ y^{2} }}. \color{purple}{\frac{\sqrt[15]{ y^{13} }}{\sqrt[15]{ y^{13} }}} \\=\frac{\sqrt[15]{ y^{13} }}{y}\\---------------\)