Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{1}}{a^{\frac{-3}{2}}}\\= a^{ 1 - (\frac{-3}{2}) }= a^{\frac{5}{2}}\\= \sqrt{ a^{5} } =|a^{2}|. \sqrt{ a } \\---------------\)
2. \(\dfrac{q^{\frac{-3}{4}}}{q^{\frac{-5}{2}}}\\= q^{ \frac{-3}{4} - (\frac{-5}{2}) }= q^{\frac{7}{4}}\\=\sqrt[4]{ q^{7} }=|q|.\sqrt[4]{ q^{3} }\\---------------\)
3. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{1}{2} - (\frac{-1}{2}) }= y^{1}\\\\---------------\)
4. \(\dfrac{y^{-1}}{y^{\frac{-1}{3}}}\\= y^{ -1 - (\frac{-1}{3}) }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
5. \(\dfrac{q^{\frac{1}{4}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{1}{4} - (\frac{-1}{3}) }= q^{\frac{7}{12}}\\=\sqrt[12]{ q^{7} }\\---------------\)
6. \(\dfrac{q^{1}}{q^{\frac{-5}{2}}}\\= q^{ 1 - (\frac{-5}{2}) }= q^{\frac{7}{2}}\\= \sqrt{ q^{7} } =|q^{3}|. \sqrt{ q } \\---------------\)
7. \(\dfrac{x^{\frac{-1}{4}}}{x^{\frac{1}{2}}}\\= x^{ \frac{-1}{4} - \frac{1}{2} }= x^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ x^{3} }}=\frac{1}{\sqrt[4]{ x^{3} }}. \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x|}\\---------------\)
8. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{2}{3}}}\\= a^{ \frac{1}{3} - \frac{2}{3} }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
9. \(\dfrac{x^{\frac{4}{5}}}{x^{\frac{-4}{3}}}\\= x^{ \frac{4}{5} - (\frac{-4}{3}) }= x^{\frac{32}{15}}\\=\sqrt[15]{ x^{32} }=x^{2}.\sqrt[15]{ x^{2} }\\---------------\)
10. \(\dfrac{q^{2}}{q^{\frac{1}{2}}}\\= q^{ 2 - \frac{1}{2} }= q^{\frac{3}{2}}\\= \sqrt{ q^{3} } =|q|. \sqrt{ q } \\---------------\)
11. \(\dfrac{y^{\frac{5}{2}}}{y^{\frac{-1}{5}}}\\= y^{ \frac{5}{2} - (\frac{-1}{5}) }= y^{\frac{27}{10}}\\=\sqrt[10]{ y^{27} }=|y^{2}|.\sqrt[10]{ y^{7} }\\---------------\)
12. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{1}{2}}}\\= x^{ \frac{2}{3} - \frac{1}{2} }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)