Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{1}}{x^{\frac{-3}{5}}}\\= x^{ 1 - (\frac{-3}{5}) }= x^{\frac{8}{5}}\\=\sqrt[5]{ x^{8} }=x.\sqrt[5]{ x^{3} }\\---------------\)
2. \(\dfrac{a^{\frac{4}{3}}}{a^{-1}}\\= a^{ \frac{4}{3} - (-1) }= a^{\frac{7}{3}}\\=\sqrt[3]{ a^{7} }=a^{2}.\sqrt[3]{ a }\\---------------\)
3. \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{1}{5}}}\\= x^{ \frac{-2}{3} - \frac{1}{5} }= x^{\frac{-13}{15}}\\=\frac{1}{\sqrt[15]{ x^{13} }}=\frac{1}{\sqrt[15]{ x^{13} }}. \color{purple}{\frac{\sqrt[15]{ x^{2} }}{\sqrt[15]{ x^{2} }}} \\=\frac{\sqrt[15]{ x^{2} }}{x}\\---------------\)
4. \(\dfrac{x^{\frac{-4}{5}}}{x^{\frac{-2}{5}}}\\= x^{ \frac{-4}{5} - (\frac{-2}{5}) }= x^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ x^{2} }}=\frac{1}{\sqrt[5]{ x^{2} }}. \color{purple}{\frac{\sqrt[5]{ x^{3} }}{\sqrt[5]{ x^{3} }}} \\=\frac{\sqrt[5]{ x^{3} }}{x}\\---------------\)
5. \(\dfrac{x^{-1}}{x^{\frac{-1}{2}}}\\= x^{ -1 - (\frac{-1}{2}) }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
6. \(\dfrac{x^{\frac{5}{4}}}{x^{\frac{1}{2}}}\\= x^{ \frac{5}{4} - \frac{1}{2} }= x^{\frac{3}{4}}\\=\sqrt[4]{ x^{3} }\\---------------\)
7. \(\dfrac{a^{1}}{a^{\frac{-5}{2}}}\\= a^{ 1 - (\frac{-5}{2}) }= a^{\frac{7}{2}}\\= \sqrt{ a^{7} } =|a^{3}|. \sqrt{ a } \\---------------\)
8. \(\dfrac{q^{\frac{-3}{5}}}{q^{\frac{3}{2}}}\\= q^{ \frac{-3}{5} - \frac{3}{2} }= q^{\frac{-21}{10}}\\=\frac{1}{\sqrt[10]{ q^{21} }}\\=\frac{1}{|q^{2}|.\sqrt[10]{ q }}=\frac{1}{|q^{2}|.\sqrt[10]{ q }} \color{purple}{\frac{\sqrt[10]{ q^{9} }}{\sqrt[10]{ q^{9} }}} \\=\frac{\sqrt[10]{ q^{9} }}{|q^{3}|}\\---------------\)
9. \(\dfrac{a^{-2}}{a^{\frac{5}{3}}}\\= a^{ -2 - \frac{5}{3} }= a^{\frac{-11}{3}}\\=\frac{1}{\sqrt[3]{ a^{11} }}\\=\frac{1}{a^{3}.\sqrt[3]{ a^{2} }}=\frac{1}{a^{3}.\sqrt[3]{ a^{2} }} \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{4}}\\---------------\)
10. \(\dfrac{y^{\frac{-4}{3}}}{y^{\frac{3}{4}}}\\= y^{ \frac{-4}{3} - \frac{3}{4} }= y^{\frac{-25}{12}}\\=\frac{1}{\sqrt[12]{ y^{25} }}\\=\frac{1}{|y^{2}|.\sqrt[12]{ y }}=\frac{1}{|y^{2}|.\sqrt[12]{ y }} \color{purple}{\frac{\sqrt[12]{ y^{11} }}{\sqrt[12]{ y^{11} }}} \\=\frac{\sqrt[12]{ y^{11} }}{|y^{3}|}\\---------------\)
11. \(\dfrac{a^{\frac{-4}{5}}}{a^{\frac{-4}{3}}}\\= a^{ \frac{-4}{5} - (\frac{-4}{3}) }= a^{\frac{8}{15}}\\=\sqrt[15]{ a^{8} }\\---------------\)
12. \(\dfrac{q^{\frac{3}{4}}}{q^{2}}\\= q^{ \frac{3}{4} - 2 }= q^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ q^{5} }}\\=\frac{1}{|q|.\sqrt[4]{ q }}=\frac{1}{|q|.\sqrt[4]{ q }} \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q^{2}|}\\---------------\)