Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-5}{3}}}{x^{\frac{-5}{6}}}\\= x^{ \frac{-5}{3} - (\frac{-5}{6}) }= x^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ x^{5} }}=\frac{1}{\sqrt[6]{ x^{5} }}. \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x|}\\---------------\)
2. \(\dfrac{a^{\frac{-3}{4}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{-3}{4} - (\frac{-1}{2}) }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
3. \(\dfrac{y^{\frac{-5}{6}}}{y^{\frac{-1}{5}}}\\= y^{ \frac{-5}{6} - (\frac{-1}{5}) }= y^{\frac{-19}{30}}\\=\frac{1}{\sqrt[30]{ y^{19} }}=\frac{1}{\sqrt[30]{ y^{19} }}. \color{purple}{\frac{\sqrt[30]{ y^{11} }}{\sqrt[30]{ y^{11} }}} \\=\frac{\sqrt[30]{ y^{11} }}{|y|}\\---------------\)
4. \(\dfrac{x^{\frac{-3}{5}}}{x^{\frac{-2}{5}}}\\= x^{ \frac{-3}{5} - (\frac{-2}{5}) }= x^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ x }}=\frac{1}{\sqrt[5]{ x }}. \color{purple}{\frac{\sqrt[5]{ x^{4} }}{\sqrt[5]{ x^{4} }}} \\=\frac{\sqrt[5]{ x^{4} }}{x}\\---------------\)
5. \(\dfrac{y^{1}}{y^{\frac{1}{6}}}\\= y^{ 1 - \frac{1}{6} }= y^{\frac{5}{6}}\\=\sqrt[6]{ y^{5} }\\---------------\)
6. \(\dfrac{x^{\frac{-5}{4}}}{x^{\frac{1}{3}}}\\= x^{ \frac{-5}{4} - \frac{1}{3} }= x^{\frac{-19}{12}}\\=\frac{1}{\sqrt[12]{ x^{19} }}\\=\frac{1}{|x|.\sqrt[12]{ x^{7} }}=\frac{1}{|x|.\sqrt[12]{ x^{7} }} \color{purple}{\frac{\sqrt[12]{ x^{5} }}{\sqrt[12]{ x^{5} }}} \\=\frac{\sqrt[12]{ x^{5} }}{|x^{2}|}\\---------------\)
7. \(\dfrac{x^{\frac{-5}{4}}}{x^{\frac{3}{4}}}\\= x^{ \frac{-5}{4} - \frac{3}{4} }= x^{-2}\\=\frac{1}{x^{2}}\\---------------\)
8. \(\dfrac{q^{-1}}{q^{\frac{5}{6}}}\\= q^{ -1 - \frac{5}{6} }= q^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ q^{11} }}\\=\frac{1}{|q|.\sqrt[6]{ q^{5} }}=\frac{1}{|q|.\sqrt[6]{ q^{5} }} \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q^{2}|}\\---------------\)
9. \(\dfrac{a^{\frac{3}{2}}}{a^{\frac{1}{6}}}\\= a^{ \frac{3}{2} - \frac{1}{6} }= a^{\frac{4}{3}}\\=\sqrt[3]{ a^{4} }=a.\sqrt[3]{ a }\\---------------\)
10. \(\dfrac{x^{\frac{-1}{5}}}{x^{\frac{2}{3}}}\\= x^{ \frac{-1}{5} - \frac{2}{3} }= x^{\frac{-13}{15}}\\=\frac{1}{\sqrt[15]{ x^{13} }}=\frac{1}{\sqrt[15]{ x^{13} }}. \color{purple}{\frac{\sqrt[15]{ x^{2} }}{\sqrt[15]{ x^{2} }}} \\=\frac{\sqrt[15]{ x^{2} }}{x}\\---------------\)
11. \(\dfrac{x^{\frac{-3}{4}}}{x^{\frac{1}{2}}}\\= x^{ \frac{-3}{4} - \frac{1}{2} }= x^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ x^{5} }}\\=\frac{1}{|x|.\sqrt[4]{ x }}=\frac{1}{|x|.\sqrt[4]{ x }} \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x^{2}|}\\---------------\)
12. \(\dfrac{q^{-1}}{q^{\frac{1}{3}}}\\= q^{ -1 - \frac{1}{3} }= q^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ q^{4} }}\\=\frac{1}{q.\sqrt[3]{ q }}=\frac{1}{q.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{2}}\\---------------\)