Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{1}}{a^{\frac{-3}{4}}}\\= a^{ 1 - (\frac{-3}{4}) }= a^{\frac{7}{4}}\\=\sqrt[4]{ a^{7} }=|a|.\sqrt[4]{ a^{3} }\\---------------\)
2. \(\dfrac{x^{1}}{x^{\frac{-4}{5}}}\\= x^{ 1 - (\frac{-4}{5}) }= x^{\frac{9}{5}}\\=\sqrt[5]{ x^{9} }=x.\sqrt[5]{ x^{4} }\\---------------\)
3. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{1}{3} - (\frac{-1}{2}) }= a^{\frac{5}{6}}\\=\sqrt[6]{ a^{5} }\\---------------\)
4. \(\dfrac{a^{\frac{-5}{6}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{-5}{6} - (\frac{-1}{2}) }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
5. \(\dfrac{a^{\frac{5}{6}}}{a^{\frac{-2}{5}}}\\= a^{ \frac{5}{6} - (\frac{-2}{5}) }= a^{\frac{37}{30}}\\=\sqrt[30]{ a^{37} }=|a|.\sqrt[30]{ a^{7} }\\---------------\)
6. \(\dfrac{q^{-2}}{q^{\frac{-3}{4}}}\\= q^{ -2 - (\frac{-3}{4}) }= q^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ q^{5} }}\\=\frac{1}{|q|.\sqrt[4]{ q }}=\frac{1}{|q|.\sqrt[4]{ q }} \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q^{2}|}\\---------------\)
7. \(\dfrac{q^{\frac{5}{4}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{5}{4} - (\frac{-2}{3}) }= q^{\frac{23}{12}}\\=\sqrt[12]{ q^{23} }=|q|.\sqrt[12]{ q^{11} }\\---------------\)
8. \(\dfrac{y^{\frac{1}{5}}}{y^{\frac{-5}{6}}}\\= y^{ \frac{1}{5} - (\frac{-5}{6}) }= y^{\frac{31}{30}}\\=\sqrt[30]{ y^{31} }=|y|.\sqrt[30]{ y }\\---------------\)
9. \(\dfrac{a^{\frac{3}{2}}}{a^{\frac{-5}{4}}}\\= a^{ \frac{3}{2} - (\frac{-5}{4}) }= a^{\frac{11}{4}}\\=\sqrt[4]{ a^{11} }=|a^{2}|.\sqrt[4]{ a^{3} }\\---------------\)
10. \(\dfrac{y^{1}}{y^{\frac{1}{3}}}\\= y^{ 1 - \frac{1}{3} }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
11. \(\dfrac{q^{\frac{2}{5}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{2}{5} - (\frac{-1}{3}) }= q^{\frac{11}{15}}\\=\sqrt[15]{ q^{11} }\\---------------\)
12. \(\dfrac{x^{\frac{4}{3}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{4}{3} - (\frac{-1}{2}) }= x^{\frac{11}{6}}\\=\sqrt[6]{ x^{11} }=|x|.\sqrt[6]{ x^{5} }\\---------------\)