Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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