Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{5}{4}}}{a^{\frac{2}{5}}}\\= a^{ \frac{5}{4} - \frac{2}{5} }= a^{\frac{17}{20}}\\=\sqrt[20]{ a^{17} }\\---------------\)
2. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{5}{4}}}\\= y^{ \frac{-1}{2} - \frac{5}{4} }= y^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[4]{ y^{3} }}=\frac{1}{|y|.\sqrt[4]{ y^{3} }} \color{purple}{\frac{\sqrt[4]{ y }}{\sqrt[4]{ y }}} \\=\frac{\sqrt[4]{ y }}{|y^{2}|}\\---------------\)
3. \(\dfrac{y^{-1}}{y^{\frac{-5}{2}}}\\= y^{ -1 - (\frac{-5}{2}) }= y^{\frac{3}{2}}\\= \sqrt{ y^{3} } =|y|. \sqrt{ y } \\---------------\)
4. \(\dfrac{y^{\frac{1}{6}}}{y^{1}}\\= y^{ \frac{1}{6} - 1 }= y^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ y^{5} }}=\frac{1}{\sqrt[6]{ y^{5} }}. \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y|}\\---------------\)
5. \(\dfrac{x^{\frac{1}{3}}}{x^{1}}\\= x^{ \frac{1}{3} - 1 }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
6. \(\dfrac{y^{\frac{3}{5}}}{y^{-1}}\\= y^{ \frac{3}{5} - (-1) }= y^{\frac{8}{5}}\\=\sqrt[5]{ y^{8} }=y.\sqrt[5]{ y^{3} }\\---------------\)
7. \(\dfrac{x^{\frac{-1}{4}}}{x^{\frac{1}{2}}}\\= x^{ \frac{-1}{4} - \frac{1}{2} }= x^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ x^{3} }}=\frac{1}{\sqrt[4]{ x^{3} }}. \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x|}\\---------------\)
8. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{3}{4}}}\\= q^{ \frac{1}{2} - \frac{3}{4} }= q^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ q }}=\frac{1}{\sqrt[4]{ q }}. \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q|}\\---------------\)
9. \(\dfrac{y^{1}}{y^{\frac{-1}{6}}}\\= y^{ 1 - (\frac{-1}{6}) }= y^{\frac{7}{6}}\\=\sqrt[6]{ y^{7} }=|y|.\sqrt[6]{ y }\\---------------\)
10. \(\dfrac{x^{\frac{-4}{3}}}{x^{\frac{-2}{3}}}\\= x^{ \frac{-4}{3} - (\frac{-2}{3}) }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
11. \(\dfrac{q^{\frac{4}{5}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{4}{5} - (\frac{-2}{3}) }= q^{\frac{22}{15}}\\=\sqrt[15]{ q^{22} }=q.\sqrt[15]{ q^{7} }\\---------------\)
12. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{1}{3}}}\\= x^{ \frac{2}{3} - \frac{1}{3} }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)