Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-4}{3}}}{x^{\frac{-4}{5}}}\\= x^{ \frac{-4}{3} - (\frac{-4}{5}) }= x^{\frac{-8}{15}}\\=\frac{1}{\sqrt[15]{ x^{8} }}=\frac{1}{\sqrt[15]{ x^{8} }}. \color{purple}{\frac{\sqrt[15]{ x^{7} }}{\sqrt[15]{ x^{7} }}} \\=\frac{\sqrt[15]{ x^{7} }}{x}\\---------------\)
2. \(\dfrac{q^{\frac{5}{2}}}{q^{\frac{-3}{4}}}\\= q^{ \frac{5}{2} - (\frac{-3}{4}) }= q^{\frac{13}{4}}\\=\sqrt[4]{ q^{13} }=|q^{3}|.\sqrt[4]{ q }\\---------------\)
3. \(\dfrac{q^{\frac{-1}{2}}}{q^{-2}}\\= q^{ \frac{-1}{2} - (-2) }= q^{\frac{3}{2}}\\= \sqrt{ q^{3} } =|q|. \sqrt{ q } \\---------------\)
4. \(\dfrac{x^{\frac{5}{2}}}{x^{\frac{-4}{5}}}\\= x^{ \frac{5}{2} - (\frac{-4}{5}) }= x^{\frac{33}{10}}\\=\sqrt[10]{ x^{33} }=|x^{3}|.\sqrt[10]{ x^{3} }\\---------------\)
5. \(\dfrac{a^{\frac{-1}{5}}}{a^{\frac{-5}{2}}}\\= a^{ \frac{-1}{5} - (\frac{-5}{2}) }= a^{\frac{23}{10}}\\=\sqrt[10]{ a^{23} }=|a^{2}|.\sqrt[10]{ a^{3} }\\---------------\)
6. \(\dfrac{x^{\frac{-3}{5}}}{x^{\frac{3}{5}}}\\= x^{ \frac{-3}{5} - \frac{3}{5} }= x^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ x^{6} }}\\=\frac{1}{x.\sqrt[5]{ x }}=\frac{1}{x.\sqrt[5]{ x }} \color{purple}{\frac{\sqrt[5]{ x^{4} }}{\sqrt[5]{ x^{4} }}} \\=\frac{\sqrt[5]{ x^{4} }}{x^{2}}\\---------------\)
7. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{1}{6}}}\\= q^{ \frac{1}{2} - \frac{1}{6} }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
8. \(\dfrac{x^{\frac{2}{5}}}{x^{\frac{-5}{2}}}\\= x^{ \frac{2}{5} - (\frac{-5}{2}) }= x^{\frac{29}{10}}\\=\sqrt[10]{ x^{29} }=|x^{2}|.\sqrt[10]{ x^{9} }\\---------------\)
9. \(\dfrac{a^{\frac{-3}{5}}}{a^{\frac{-4}{3}}}\\= a^{ \frac{-3}{5} - (\frac{-4}{3}) }= a^{\frac{11}{15}}\\=\sqrt[15]{ a^{11} }\\---------------\)
10. \(\dfrac{a^{\frac{-1}{3}}}{a^{-1}}\\= a^{ \frac{-1}{3} - (-1) }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
11. \(\dfrac{y^{\frac{-1}{6}}}{y^{-1}}\\= y^{ \frac{-1}{6} - (-1) }= y^{\frac{5}{6}}\\=\sqrt[6]{ y^{5} }\\---------------\)
12. \(\dfrac{a^{\frac{1}{2}}}{a^{1}}\\= a^{ \frac{1}{2} - 1 }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)