Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-3}{4}}}{a^{\frac{1}{5}}}\\= a^{ \frac{-3}{4} - \frac{1}{5} }= a^{\frac{-19}{20}}\\=\frac{1}{\sqrt[20]{ a^{19} }}=\frac{1}{\sqrt[20]{ a^{19} }}. \color{purple}{\frac{\sqrt[20]{ a }}{\sqrt[20]{ a }}} \\=\frac{\sqrt[20]{ a }}{|a|}\\---------------\)
2. \(\dfrac{y^{1}}{y^{\frac{-5}{3}}}\\= y^{ 1 - (\frac{-5}{3}) }= y^{\frac{8}{3}}\\=\sqrt[3]{ y^{8} }=y^{2}.\sqrt[3]{ y^{2} }\\---------------\)
3. \(\dfrac{y^{\frac{3}{4}}}{y^{\frac{5}{3}}}\\= y^{ \frac{3}{4} - \frac{5}{3} }= y^{\frac{-11}{12}}\\=\frac{1}{\sqrt[12]{ y^{11} }}=\frac{1}{\sqrt[12]{ y^{11} }}. \color{purple}{\frac{\sqrt[12]{ y }}{\sqrt[12]{ y }}} \\=\frac{\sqrt[12]{ y }}{|y|}\\---------------\)
4. \(\dfrac{a^{-1}}{a^{\frac{1}{6}}}\\= a^{ -1 - \frac{1}{6} }= a^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ a^{7} }}\\=\frac{1}{|a|.\sqrt[6]{ a }}=\frac{1}{|a|.\sqrt[6]{ a }} \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a^{2}|}\\---------------\)
5. \(\dfrac{q^{\frac{-3}{2}}}{q^{\frac{1}{6}}}\\= q^{ \frac{-3}{2} - \frac{1}{6} }= q^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ q^{5} }}\\=\frac{1}{q.\sqrt[3]{ q^{2} }}=\frac{1}{q.\sqrt[3]{ q^{2} }} \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{2}}\\---------------\)
6. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{3}{5}}}\\= x^{ \frac{1}{2} - \frac{3}{5} }= x^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ x }}=\frac{1}{\sqrt[10]{ x }}. \color{purple}{\frac{\sqrt[10]{ x^{9} }}{\sqrt[10]{ x^{9} }}} \\=\frac{\sqrt[10]{ x^{9} }}{|x|}\\---------------\)
7. \(\dfrac{x^{\frac{5}{4}}}{x^{\frac{3}{4}}}\\= x^{ \frac{5}{4} - \frac{3}{4} }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
8. \(\dfrac{q^{\frac{-4}{3}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{-4}{3} - (\frac{-1}{2}) }= q^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ q^{5} }}=\frac{1}{\sqrt[6]{ q^{5} }}. \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q|}\\---------------\)
9. \(\dfrac{a^{\frac{1}{6}}}{a^{\frac{3}{4}}}\\= a^{ \frac{1}{6} - \frac{3}{4} }= a^{\frac{-7}{12}}\\=\frac{1}{\sqrt[12]{ a^{7} }}=\frac{1}{\sqrt[12]{ a^{7} }}. \color{purple}{\frac{\sqrt[12]{ a^{5} }}{\sqrt[12]{ a^{5} }}} \\=\frac{\sqrt[12]{ a^{5} }}{|a|}\\---------------\)
10. \(\dfrac{x^{1}}{x^{\frac{-3}{4}}}\\= x^{ 1 - (\frac{-3}{4}) }= x^{\frac{7}{4}}\\=\sqrt[4]{ x^{7} }=|x|.\sqrt[4]{ x^{3} }\\---------------\)
11. \(\dfrac{a^{\frac{-5}{4}}}{a^{\frac{5}{4}}}\\= a^{ \frac{-5}{4} - \frac{5}{4} }= a^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ a^{5} } }\\=\frac{1}{|a^{2}|. \sqrt{ a } }=\frac{1}{|a^{2}|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{3}|}\\---------------\)
12. \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{-3}{5}}}\\= x^{ \frac{-2}{3} - (\frac{-3}{5}) }= x^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ x }}=\frac{1}{\sqrt[15]{ x }}. \color{purple}{\frac{\sqrt[15]{ x^{14} }}{\sqrt[15]{ x^{14} }}} \\=\frac{\sqrt[15]{ x^{14} }}{x}\\---------------\)