Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{1}}{a^{2}}\\= a^{ 1 - 2 }= a^{-1}\\=\frac{1}{a}\\---------------\)
2. \(\dfrac{y^{\frac{3}{4}}}{y^{\frac{4}{5}}}\\= y^{ \frac{3}{4} - \frac{4}{5} }= y^{\frac{-1}{20}}\\=\frac{1}{\sqrt[20]{ y }}=\frac{1}{\sqrt[20]{ y }}. \color{purple}{\frac{\sqrt[20]{ y^{19} }}{\sqrt[20]{ y^{19} }}} \\=\frac{\sqrt[20]{ y^{19} }}{|y|}\\---------------\)
3. \(\dfrac{x^{\frac{1}{4}}}{x^{2}}\\= x^{ \frac{1}{4} - 2 }= x^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ x^{7} }}\\=\frac{1}{|x|.\sqrt[4]{ x^{3} }}=\frac{1}{|x|.\sqrt[4]{ x^{3} }} \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x^{2}|}\\---------------\)
4. \(\dfrac{y^{-1}}{y^{-2}}\\= y^{ -1 - (-2) }= y^{1}\\\\---------------\)
5. \(\dfrac{y^{\frac{-4}{5}}}{y^{\frac{3}{5}}}\\= y^{ \frac{-4}{5} - \frac{3}{5} }= y^{\frac{-7}{5}}\\=\frac{1}{\sqrt[5]{ y^{7} }}\\=\frac{1}{y.\sqrt[5]{ y^{2} }}=\frac{1}{y.\sqrt[5]{ y^{2} }} \color{purple}{\frac{\sqrt[5]{ y^{3} }}{\sqrt[5]{ y^{3} }}} \\=\frac{\sqrt[5]{ y^{3} }}{y^{2}}\\---------------\)
6. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{4}{5}}}\\= y^{ \frac{2}{3} - \frac{4}{5} }= y^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ y^{2} }}=\frac{1}{\sqrt[15]{ y^{2} }}. \color{purple}{\frac{\sqrt[15]{ y^{13} }}{\sqrt[15]{ y^{13} }}} \\=\frac{\sqrt[15]{ y^{13} }}{y}\\---------------\)
7. \(\dfrac{y^{-2}}{y^{\frac{-3}{4}}}\\= y^{ -2 - (\frac{-3}{4}) }= y^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ y^{5} }}\\=\frac{1}{|y|.\sqrt[4]{ y }}=\frac{1}{|y|.\sqrt[4]{ y }} \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y^{2}|}\\---------------\)
8. \(\dfrac{x^{\frac{-5}{6}}}{x^{\frac{1}{3}}}\\= x^{ \frac{-5}{6} - \frac{1}{3} }= x^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ x^{7} }}\\=\frac{1}{|x|.\sqrt[6]{ x }}=\frac{1}{|x|.\sqrt[6]{ x }} \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x^{2}|}\\---------------\)
9. \(\dfrac{x^{\frac{-3}{2}}}{x^{\frac{-1}{6}}}\\= x^{ \frac{-3}{2} - (\frac{-1}{6}) }= x^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ x^{4} }}\\=\frac{1}{x.\sqrt[3]{ x }}=\frac{1}{x.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{2}}\\---------------\)
10. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{4}{3}}}\\= q^{ \frac{1}{2} - \frac{4}{3} }= q^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ q^{5} }}=\frac{1}{\sqrt[6]{ q^{5} }}. \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q|}\\---------------\)
11. \(\dfrac{q^{-1}}{q^{\frac{1}{2}}}\\= q^{ -1 - \frac{1}{2} }= q^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ q^{3} } }\\=\frac{1}{|q|. \sqrt{ q } }=\frac{1}{|q|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{2}|}\\---------------\)
12. \(\dfrac{a^{\frac{1}{5}}}{a^{\frac{4}{3}}}\\= a^{ \frac{1}{5} - \frac{4}{3} }= a^{\frac{-17}{15}}\\=\frac{1}{\sqrt[15]{ a^{17} }}\\=\frac{1}{a.\sqrt[15]{ a^{2} }}=\frac{1}{a.\sqrt[15]{ a^{2} }} \color{purple}{\frac{\sqrt[15]{ a^{13} }}{\sqrt[15]{ a^{13} }}} \\=\frac{\sqrt[15]{ a^{13} }}{a^{2}}\\---------------\)