Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-3}{5}}}{q^{\frac{1}{2}}}\\= q^{ \frac{-3}{5} - \frac{1}{2} }= q^{\frac{-11}{10}}\\=\frac{1}{\sqrt[10]{ q^{11} }}\\=\frac{1}{|q|.\sqrt[10]{ q }}=\frac{1}{|q|.\sqrt[10]{ q }} \color{purple}{\frac{\sqrt[10]{ q^{9} }}{\sqrt[10]{ q^{9} }}} \\=\frac{\sqrt[10]{ q^{9} }}{|q^{2}|}\\---------------\)
2. \(\dfrac{y^{\frac{4}{5}}}{y^{\frac{5}{4}}}\\= y^{ \frac{4}{5} - \frac{5}{4} }= y^{\frac{-9}{20}}\\=\frac{1}{\sqrt[20]{ y^{9} }}=\frac{1}{\sqrt[20]{ y^{9} }}. \color{purple}{\frac{\sqrt[20]{ y^{11} }}{\sqrt[20]{ y^{11} }}} \\=\frac{\sqrt[20]{ y^{11} }}{|y|}\\---------------\)
3. \(\dfrac{q^{\frac{-5}{6}}}{q^{\frac{-1}{4}}}\\= q^{ \frac{-5}{6} - (\frac{-1}{4}) }= q^{\frac{-7}{12}}\\=\frac{1}{\sqrt[12]{ q^{7} }}=\frac{1}{\sqrt[12]{ q^{7} }}. \color{purple}{\frac{\sqrt[12]{ q^{5} }}{\sqrt[12]{ q^{5} }}} \\=\frac{\sqrt[12]{ q^{5} }}{|q|}\\---------------\)
4. \(\dfrac{a^{1}}{a^{-1}}\\= a^{ 1 - (-1) }= a^{2}\\\\---------------\)
5. \(\dfrac{x^{\frac{-5}{6}}}{x^{1}}\\= x^{ \frac{-5}{6} - 1 }= x^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ x^{11} }}\\=\frac{1}{|x|.\sqrt[6]{ x^{5} }}=\frac{1}{|x|.\sqrt[6]{ x^{5} }} \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x^{2}|}\\---------------\)
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. \(\dfrac{a^{\frac{2}{5}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{2}{5} - (\frac{-1}{2}) }= a^{\frac{9}{10}}\\=\sqrt[10]{ a^{9} }\\---------------\)
8. \(\dfrac{a^{\frac{3}{2}}}{a^{\frac{2}{5}}}\\= a^{ \frac{3}{2} - \frac{2}{5} }= a^{\frac{11}{10}}\\=\sqrt[10]{ a^{11} }=|a|.\sqrt[10]{ a }\\---------------\)
9. \(\dfrac{a^{\frac{-2}{3}}}{a^{1}}\\= a^{ \frac{-2}{3} - 1 }= a^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ a^{5} }}\\=\frac{1}{a.\sqrt[3]{ a^{2} }}=\frac{1}{a.\sqrt[3]{ a^{2} }} \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{2}}\\---------------\)
10. \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{-4}{5}}}\\= x^{ \frac{-2}{3} - (\frac{-4}{5}) }= x^{\frac{2}{15}}\\=\sqrt[15]{ x^{2} }\\---------------\)
11. \(\dfrac{a^{\frac{-3}{4}}}{a^{\frac{1}{2}}}\\= a^{ \frac{-3}{4} - \frac{1}{2} }= a^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ a^{5} }}\\=\frac{1}{|a|.\sqrt[4]{ a }}=\frac{1}{|a|.\sqrt[4]{ a }} \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a^{2}|}\\---------------\)
12. \(\dfrac{a^{\frac{5}{4}}}{a^{\frac{1}{5}}}\\= a^{ \frac{5}{4} - \frac{1}{5} }= a^{\frac{21}{20}}\\=\sqrt[20]{ a^{21} }=|a|.\sqrt[20]{ a }\\---------------\)