Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-5}{3}}}{q^{\frac{-3}{5}}}\\= q^{ \frac{-5}{3} - (\frac{-3}{5}) }= q^{\frac{-16}{15}}\\=\frac{1}{\sqrt[15]{ q^{16} }}\\=\frac{1}{q.\sqrt[15]{ q }}=\frac{1}{q.\sqrt[15]{ q }} \color{purple}{\frac{\sqrt[15]{ q^{14} }}{\sqrt[15]{ q^{14} }}} \\=\frac{\sqrt[15]{ q^{14} }}{q^{2}}\\---------------\)
2. \(\dfrac{x^{-1}}{x^{\frac{1}{2}}}\\= x^{ -1 - \frac{1}{2} }= x^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ x^{3} } }\\=\frac{1}{|x|. \sqrt{ x } }=\frac{1}{|x|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{2}|}\\---------------\)
3. \(\dfrac{x^{\frac{-5}{3}}}{x^{\frac{-5}{4}}}\\= x^{ \frac{-5}{3} - (\frac{-5}{4}) }= x^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ x^{5} }}=\frac{1}{\sqrt[12]{ x^{5} }}. \color{purple}{\frac{\sqrt[12]{ x^{7} }}{\sqrt[12]{ x^{7} }}} \\=\frac{\sqrt[12]{ x^{7} }}{|x|}\\---------------\)
4. \(\dfrac{y^{\frac{-5}{3}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{-5}{3} - (\frac{-2}{3}) }= y^{-1}\\=\frac{1}{y}\\---------------\)
5. \(\dfrac{q^{\frac{-3}{2}}}{q^{\frac{5}{2}}}\\= q^{ \frac{-3}{2} - \frac{5}{2} }= q^{-4}\\=\frac{1}{q^{4}}\\---------------\)
6. \(\dfrac{a^{\frac{3}{5}}}{a^{\frac{-4}{3}}}\\= a^{ \frac{3}{5} - (\frac{-4}{3}) }= a^{\frac{29}{15}}\\=\sqrt[15]{ a^{29} }=a.\sqrt[15]{ a^{14} }\\---------------\)
7. \(\dfrac{x^{\frac{1}{3}}}{x^{\frac{5}{3}}}\\= x^{ \frac{1}{3} - \frac{5}{3} }= x^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ x^{4} }}\\=\frac{1}{x.\sqrt[3]{ x }}=\frac{1}{x.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{2}}\\---------------\)
8. \(\dfrac{x^{\frac{-3}{2}}}{x^{\frac{-1}{4}}}\\= x^{ \frac{-3}{2} - (\frac{-1}{4}) }= x^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ x^{5} }}\\=\frac{1}{|x|.\sqrt[4]{ x }}=\frac{1}{|x|.\sqrt[4]{ x }} \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x^{2}|}\\---------------\)
9. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{-1}{2} - (\frac{-2}{3}) }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
10. \(\dfrac{y^{\frac{-5}{4}}}{y^{1}}\\= y^{ \frac{-5}{4} - 1 }= y^{\frac{-9}{4}}\\=\frac{1}{\sqrt[4]{ y^{9} }}\\=\frac{1}{|y^{2}|.\sqrt[4]{ y }}=\frac{1}{|y^{2}|.\sqrt[4]{ y }} \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y^{3}|}\\---------------\)
11. \(\dfrac{a^{\frac{-1}{4}}}{a^{1}}\\= a^{ \frac{-1}{4} - 1 }= a^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ a^{5} }}\\=\frac{1}{|a|.\sqrt[4]{ a }}=\frac{1}{|a|.\sqrt[4]{ a }} \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a^{2}|}\\---------------\)
12. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{-2}{5}}}\\= x^{ \frac{1}{2} - (\frac{-2}{5}) }= x^{\frac{9}{10}}\\=\sqrt[10]{ x^{9} }\\---------------\)