Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{1}}{a^{\frac{-5}{2}}}\\= a^{ 1 - (\frac{-5}{2}) }= a^{\frac{7}{2}}\\= \sqrt{ a^{7} } =|a^{3}|. \sqrt{ a } \\---------------\)
2. \(\dfrac{y^{-1}}{y^{\frac{-1}{3}}}\\= y^{ -1 - (\frac{-1}{3}) }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
3. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{-5}{4}}}\\= y^{ \frac{-1}{3} - (\frac{-5}{4}) }= y^{\frac{11}{12}}\\=\sqrt[12]{ y^{11} }\\---------------\)
4. \(\dfrac{q^{\frac{3}{4}}}{q^{\frac{-1}{5}}}\\= q^{ \frac{3}{4} - (\frac{-1}{5}) }= q^{\frac{19}{20}}\\=\sqrt[20]{ q^{19} }\\---------------\)
5. \(\dfrac{q^{\frac{4}{3}}}{q^{-2}}\\= q^{ \frac{4}{3} - (-2) }= q^{\frac{10}{3}}\\=\sqrt[3]{ q^{10} }=q^{3}.\sqrt[3]{ q }\\---------------\)
6. \(\dfrac{a^{\frac{5}{2}}}{a^{\frac{-4}{5}}}\\= a^{ \frac{5}{2} - (\frac{-4}{5}) }= a^{\frac{33}{10}}\\=\sqrt[10]{ a^{33} }=|a^{3}|.\sqrt[10]{ a^{3} }\\---------------\)
7. \(\dfrac{q^{\frac{3}{5}}}{q^{\frac{-5}{6}}}\\= q^{ \frac{3}{5} - (\frac{-5}{6}) }= q^{\frac{43}{30}}\\=\sqrt[30]{ q^{43} }=|q|.\sqrt[30]{ q^{13} }\\---------------\)
8. \(\dfrac{q^{\frac{-1}{2}}}{q^{1}}\\= q^{ \frac{-1}{2} - 1 }= q^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ q^{3} } }\\=\frac{1}{|q|. \sqrt{ q } }=\frac{1}{|q|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{2}|}\\---------------\)
9. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{-5}{2}}}\\= x^{ \frac{2}{3} - (\frac{-5}{2}) }= x^{\frac{19}{6}}\\=\sqrt[6]{ x^{19} }=|x^{3}|.\sqrt[6]{ x }\\---------------\)
10. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{-5}{4}}}\\= x^{ \frac{-1}{2} - (\frac{-5}{4}) }= x^{\frac{3}{4}}\\=\sqrt[4]{ x^{3} }\\---------------\)
11. \(\dfrac{x^{\frac{-4}{3}}}{x^{\frac{2}{3}}}\\= x^{ \frac{-4}{3} - \frac{2}{3} }= x^{-2}\\=\frac{1}{x^{2}}\\---------------\)
12. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{-1}{2} - (\frac{-2}{3}) }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)