Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{1}}{a^{\frac{-4}{5}}}\\= a^{ 1 - (\frac{-4}{5}) }= a^{\frac{9}{5}}\\=\sqrt[5]{ a^{9} }=a.\sqrt[5]{ a^{4} }\\---------------\)
2. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{-1}{4}}}\\= x^{ \frac{1}{2} - (\frac{-1}{4}) }= x^{\frac{3}{4}}\\=\sqrt[4]{ x^{3} }\\---------------\)
3. \(\dfrac{q^{1}}{q^{\frac{-4}{3}}}\\= q^{ 1 - (\frac{-4}{3}) }= q^{\frac{7}{3}}\\=\sqrt[3]{ q^{7} }=q^{2}.\sqrt[3]{ q }\\---------------\)
4. \(\dfrac{a^{\frac{-5}{6}}}{a^{\frac{1}{4}}}\\= a^{ \frac{-5}{6} - \frac{1}{4} }= a^{\frac{-13}{12}}\\=\frac{1}{\sqrt[12]{ a^{13} }}\\=\frac{1}{|a|.\sqrt[12]{ a }}=\frac{1}{|a|.\sqrt[12]{ a }} \color{purple}{\frac{\sqrt[12]{ a^{11} }}{\sqrt[12]{ a^{11} }}} \\=\frac{\sqrt[12]{ a^{11} }}{|a^{2}|}\\---------------\)
5. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{-5}{6}}}\\= a^{ \frac{-1}{2} - (\frac{-5}{6}) }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
6. \(\dfrac{a^{\frac{-3}{4}}}{a^{-2}}\\= a^{ \frac{-3}{4} - (-2) }= a^{\frac{5}{4}}\\=\sqrt[4]{ a^{5} }=|a|.\sqrt[4]{ a }\\---------------\)
7. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{-3}{2}}}\\= x^{ \frac{-1}{3} - (\frac{-3}{2}) }= x^{\frac{7}{6}}\\=\sqrt[6]{ x^{7} }=|x|.\sqrt[6]{ x }\\---------------\)
8. \(\dfrac{y^{\frac{-5}{4}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{-5}{4} - (\frac{-2}{3}) }= y^{\frac{-7}{12}}\\=\frac{1}{\sqrt[12]{ y^{7} }}=\frac{1}{\sqrt[12]{ y^{7} }}. \color{purple}{\frac{\sqrt[12]{ y^{5} }}{\sqrt[12]{ y^{5} }}} \\=\frac{\sqrt[12]{ y^{5} }}{|y|}\\---------------\)
9. \(\dfrac{a^{\frac{-1}{6}}}{a^{\frac{-1}{5}}}\\= a^{ \frac{-1}{6} - (\frac{-1}{5}) }= a^{\frac{1}{30}}\\=\sqrt[30]{ a }\\---------------\)
10. \(\dfrac{x^{\frac{2}{5}}}{x^{\frac{-5}{6}}}\\= x^{ \frac{2}{5} - (\frac{-5}{6}) }= x^{\frac{37}{30}}\\=\sqrt[30]{ x^{37} }=|x|.\sqrt[30]{ x^{7} }\\---------------\)
11. \(\dfrac{a^{1}}{a^{-1}}\\= a^{ 1 - (-1) }= a^{2}\\\\---------------\)
12. \(\dfrac{q^{\frac{-1}{6}}}{q^{\frac{-5}{3}}}\\= q^{ \frac{-1}{6} - (\frac{-5}{3}) }= q^{\frac{3}{2}}\\= \sqrt{ q^{3} } =|q|. \sqrt{ q } \\---------------\)