Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{1}{4}}}{a^{\frac{-2}{5}}}\\= a^{ \frac{1}{4} - (\frac{-2}{5}) }= a^{\frac{13}{20}}\\=\sqrt[20]{ a^{13} }\\---------------\)
2. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{-3}{4}}}\\= y^{ \frac{1}{2} - (\frac{-3}{4}) }= y^{\frac{5}{4}}\\=\sqrt[4]{ y^{5} }=|y|.\sqrt[4]{ y }\\---------------\)
3. \(\dfrac{x^{-1}}{x^{\frac{-5}{2}}}\\= x^{ -1 - (\frac{-5}{2}) }= x^{\frac{3}{2}}\\= \sqrt{ x^{3} } =|x|. \sqrt{ x } \\---------------\)
4. \(\dfrac{a^{\frac{1}{4}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{1}{4} - (\frac{-1}{2}) }= a^{\frac{3}{4}}\\=\sqrt[4]{ a^{3} }\\---------------\)
5. \(\dfrac{x^{\frac{1}{5}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{1}{5} - (\frac{-1}{3}) }= x^{\frac{8}{15}}\\=\sqrt[15]{ x^{8} }\\---------------\)
6. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{-4}{3}}}\\= q^{ \frac{1}{3} - (\frac{-4}{3}) }= q^{\frac{5}{3}}\\=\sqrt[3]{ q^{5} }=q.\sqrt[3]{ q^{2} }\\---------------\)
7. \(\dfrac{a^{\frac{4}{5}}}{a^{\frac{2}{3}}}\\= a^{ \frac{4}{5} - \frac{2}{3} }= a^{\frac{2}{15}}\\=\sqrt[15]{ a^{2} }\\---------------\)
8. \(\dfrac{a^{\frac{1}{3}}}{a^{-1}}\\= a^{ \frac{1}{3} - (-1) }= a^{\frac{4}{3}}\\=\sqrt[3]{ a^{4} }=a.\sqrt[3]{ a }\\---------------\)
9. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{-2}{5}}}\\= q^{ \frac{-1}{3} - (\frac{-2}{5}) }= q^{\frac{1}{15}}\\=\sqrt[15]{ q }\\---------------\)
10. \(\dfrac{x^{\frac{-4}{3}}}{x^{\frac{-3}{4}}}\\= x^{ \frac{-4}{3} - (\frac{-3}{4}) }= x^{\frac{-7}{12}}\\=\frac{1}{\sqrt[12]{ x^{7} }}=\frac{1}{\sqrt[12]{ x^{7} }}. \color{purple}{\frac{\sqrt[12]{ x^{5} }}{\sqrt[12]{ x^{5} }}} \\=\frac{\sqrt[12]{ x^{5} }}{|x|}\\---------------\)
11. \(\dfrac{q^{-1}}{q^{\frac{-3}{2}}}\\= q^{ -1 - (\frac{-3}{2}) }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
12. \(\dfrac{x^{\frac{1}{3}}}{x^{\frac{1}{5}}}\\= x^{ \frac{1}{3} - \frac{1}{5} }= x^{\frac{2}{15}}\\=\sqrt[15]{ x^{2} }\\---------------\)