Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-3}{5}}}{y^{\frac{5}{4}}}\\= y^{ \frac{-3}{5} - \frac{5}{4} }= y^{\frac{-37}{20}}\\=\frac{1}{\sqrt[20]{ y^{37} }}\\=\frac{1}{|y|.\sqrt[20]{ y^{17} }}=\frac{1}{|y|.\sqrt[20]{ y^{17} }} \color{purple}{\frac{\sqrt[20]{ y^{3} }}{\sqrt[20]{ y^{3} }}} \\=\frac{\sqrt[20]{ y^{3} }}{|y^{2}|}\\---------------\)
2. \(\dfrac{q^{\frac{-4}{5}}}{q^{\frac{2}{5}}}\\= q^{ \frac{-4}{5} - \frac{2}{5} }= q^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ q^{6} }}\\=\frac{1}{q.\sqrt[5]{ q }}=\frac{1}{q.\sqrt[5]{ q }} \color{purple}{\frac{\sqrt[5]{ q^{4} }}{\sqrt[5]{ q^{4} }}} \\=\frac{\sqrt[5]{ q^{4} }}{q^{2}}\\---------------\)
3. \(\dfrac{a^{2}}{a^{\frac{3}{2}}}\\= a^{ 2 - \frac{3}{2} }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
4. \(\dfrac{x^{\frac{-1}{6}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{-1}{6} - (\frac{-1}{3}) }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
5. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{1}{2}}}\\= q^{ \frac{1}{3} - \frac{1}{2} }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)
6. \(\dfrac{y^{\frac{-1}{6}}}{y^{\frac{-5}{6}}}\\= y^{ \frac{-1}{6} - (\frac{-5}{6}) }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
7. \(\dfrac{a^{\frac{4}{5}}}{a^{1}}\\= a^{ \frac{4}{5} - 1 }= a^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ a }}=\frac{1}{\sqrt[5]{ a }}. \color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a}\\---------------\)
8. \(\dfrac{a^{\frac{-3}{4}}}{a^{\frac{1}{2}}}\\= a^{ \frac{-3}{4} - \frac{1}{2} }= a^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ a^{5} }}\\=\frac{1}{|a|.\sqrt[4]{ a }}=\frac{1}{|a|.\sqrt[4]{ a }} \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a^{2}|}\\---------------\)
9. \(\dfrac{a^{-1}}{a^{\frac{5}{6}}}\\= a^{ -1 - \frac{5}{6} }= a^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ a^{11} }}\\=\frac{1}{|a|.\sqrt[6]{ a^{5} }}=\frac{1}{|a|.\sqrt[6]{ a^{5} }} \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a^{2}|}\\---------------\)
10. \(\dfrac{q^{\frac{-2}{3}}}{q^{1}}\\= q^{ \frac{-2}{3} - 1 }= q^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ q^{5} }}\\=\frac{1}{q.\sqrt[3]{ q^{2} }}=\frac{1}{q.\sqrt[3]{ q^{2} }} \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{2}}\\---------------\)
11. \(\dfrac{y^{\frac{5}{6}}}{y^{-1}}\\= y^{ \frac{5}{6} - (-1) }= y^{\frac{11}{6}}\\=\sqrt[6]{ y^{11} }=|y|.\sqrt[6]{ y^{5} }\\---------------\)
12. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{2}{3}}}\\= q^{ \frac{2}{3} - \frac{2}{3} }= q^{0}\\=1\\---------------\)