Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{1}}{q^{\frac{3}{5}}}\\= q^{ 1 - \frac{3}{5} }= q^{\frac{2}{5}}\\=\sqrt[5]{ q^{2} }\\---------------\)
2. \(\dfrac{y^{\frac{1}{3}}}{y^{\frac{1}{2}}}\\= y^{ \frac{1}{3} - \frac{1}{2} }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
3. \(\dfrac{q^{\frac{-3}{5}}}{q^{\frac{2}{5}}}\\= q^{ \frac{-3}{5} - \frac{2}{5} }= q^{-1}\\=\frac{1}{q}\\---------------\)
4. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{1}{3} - (\frac{-2}{3}) }= q^{1}\\\\---------------\)
5. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{1}{2} - (\frac{-1}{3}) }= y^{\frac{5}{6}}\\=\sqrt[6]{ y^{5} }\\---------------\)
6. \(\dfrac{x^{\frac{1}{3}}}{x^{\frac{2}{5}}}\\= x^{ \frac{1}{3} - \frac{2}{5} }= x^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ x }}=\frac{1}{\sqrt[15]{ x }}. \color{purple}{\frac{\sqrt[15]{ x^{14} }}{\sqrt[15]{ x^{14} }}} \\=\frac{\sqrt[15]{ x^{14} }}{x}\\---------------\)
7. \(\dfrac{a^{\frac{1}{5}}}{a^{\frac{-2}{5}}}\\= a^{ \frac{1}{5} - (\frac{-2}{5}) }= a^{\frac{3}{5}}\\=\sqrt[5]{ a^{3} }\\---------------\)
8. \(\dfrac{a^{\frac{4}{5}}}{a^{\frac{4}{3}}}\\= a^{ \frac{4}{5} - \frac{4}{3} }= a^{\frac{-8}{15}}\\=\frac{1}{\sqrt[15]{ a^{8} }}=\frac{1}{\sqrt[15]{ a^{8} }}. \color{purple}{\frac{\sqrt[15]{ a^{7} }}{\sqrt[15]{ a^{7} }}} \\=\frac{\sqrt[15]{ a^{7} }}{a}\\---------------\)
9. \(\dfrac{x^{\frac{-5}{4}}}{x^{\frac{-1}{4}}}\\= x^{ \frac{-5}{4} - (\frac{-1}{4}) }= x^{-1}\\=\frac{1}{x}\\---------------\)
10. \(\dfrac{q^{-2}}{q^{\frac{3}{2}}}\\= q^{ -2 - \frac{3}{2} }= q^{\frac{-7}{2}}\\=\frac{1}{ \sqrt{ q^{7} } }\\=\frac{1}{|q^{3}|. \sqrt{ q } }=\frac{1}{|q^{3}|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{4}|}\\---------------\)
11. \(\dfrac{x^{\frac{3}{4}}}{x^{\frac{-5}{3}}}\\= x^{ \frac{3}{4} - (\frac{-5}{3}) }= x^{\frac{29}{12}}\\=\sqrt[12]{ x^{29} }=|x^{2}|.\sqrt[12]{ x^{5} }\\---------------\)
12. \(\dfrac{x^{\frac{-3}{2}}}{x^{\frac{5}{2}}}\\= x^{ \frac{-3}{2} - \frac{5}{2} }= x^{-4}\\=\frac{1}{x^{4}}\\---------------\)