Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{4}{3}}}{y^{\frac{-3}{4}}}\\= y^{ \frac{4}{3} - (\frac{-3}{4}) }= y^{\frac{25}{12}}\\=\sqrt[12]{ y^{25} }=|y^{2}|.\sqrt[12]{ y }\\---------------\)
2. \(\dfrac{a^{\frac{-1}{4}}}{a^{\frac{5}{2}}}\\= a^{ \frac{-1}{4} - \frac{5}{2} }= a^{\frac{-11}{4}}\\=\frac{1}{\sqrt[4]{ a^{11} }}\\=\frac{1}{|a^{2}|.\sqrt[4]{ a^{3} }}=\frac{1}{|a^{2}|.\sqrt[4]{ a^{3} }} \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a^{3}|}\\---------------\)
3. \(\dfrac{y^{\frac{-4}{5}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{-4}{5} - (\frac{-2}{3}) }= y^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ y^{2} }}=\frac{1}{\sqrt[15]{ y^{2} }}. \color{purple}{\frac{\sqrt[15]{ y^{13} }}{\sqrt[15]{ y^{13} }}} \\=\frac{\sqrt[15]{ y^{13} }}{y}\\---------------\)
4. \(\dfrac{x^{-2}}{x^{\frac{-1}{4}}}\\= x^{ -2 - (\frac{-1}{4}) }= x^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ x^{7} }}\\=\frac{1}{|x|.\sqrt[4]{ x^{3} }}=\frac{1}{|x|.\sqrt[4]{ x^{3} }} \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x^{2}|}\\---------------\)
5. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{-1}{2} - (\frac{-1}{2}) }= y^{0}\\=1\\---------------\)
6. \(\dfrac{x^{\frac{4}{3}}}{x^{\frac{-2}{3}}}\\= x^{ \frac{4}{3} - (\frac{-2}{3}) }= x^{2}\\\\---------------\)
7. \(\dfrac{x^{\frac{-5}{6}}}{x^{\frac{-3}{4}}}\\= x^{ \frac{-5}{6} - (\frac{-3}{4}) }= x^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ x }}=\frac{1}{\sqrt[12]{ x }}. \color{purple}{\frac{\sqrt[12]{ x^{11} }}{\sqrt[12]{ x^{11} }}} \\=\frac{\sqrt[12]{ x^{11} }}{|x|}\\---------------\)
8. \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{1}{6}}}\\= x^{ \frac{-2}{3} - \frac{1}{6} }= x^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ x^{5} }}=\frac{1}{\sqrt[6]{ x^{5} }}. \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x|}\\---------------\)
9. \(\dfrac{y^{\frac{5}{6}}}{y^{\frac{5}{6}}}\\= y^{ \frac{5}{6} - \frac{5}{6} }= y^{0}\\=1\\---------------\)
10. \(\dfrac{q^{\frac{2}{5}}}{q^{\frac{2}{3}}}\\= q^{ \frac{2}{5} - \frac{2}{3} }= q^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ q^{4} }}=\frac{1}{\sqrt[15]{ q^{4} }}. \color{purple}{\frac{\sqrt[15]{ q^{11} }}{\sqrt[15]{ q^{11} }}} \\=\frac{\sqrt[15]{ q^{11} }}{q}\\---------------\)
11. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{1}{2} - (\frac{-2}{3}) }= q^{\frac{7}{6}}\\=\sqrt[6]{ q^{7} }=|q|.\sqrt[6]{ q }\\---------------\)
12. \(\dfrac{a^{1}}{a^{\frac{-5}{2}}}\\= a^{ 1 - (\frac{-5}{2}) }= a^{\frac{7}{2}}\\= \sqrt{ a^{7} } =|a^{3}|. \sqrt{ a } \\---------------\)